UNITED STATES

DEPARTMENT OF COMMERCE

Carlos M. Gutierrez

Secretary

NATIONAL OCEANIC AND

ATMOSPHERIC ADMINISTRATION

VADM Conrad C. Lautenbacher, Jr.

Under Secretary for Oceans

and Atmosphere/Administrator

Office of Oceanic and 

Atmospheric Research

Richard W. Spinrad

Assistant Administrator

NOAA Technical Memorandum OAR PMEL-141

DEVELOPING TSUNAMI FORECAST INUNDATION MODELS FOR HAWAII:

PROCEDURES AND TESTING

Liujuan Tang1,2

Christopher D. Chamberlin1,2

Vasily V. Titov1,2

1

Joint Institute for the Study of the Atmosphere and Ocean (JISAO)

University of Washington, Seattle, WA

2

Pacific Marine Environmental Laboratory

Seattle, WA

Pacific Marine Environmental Laboratory

Seattle, WA

August 2008
NOTICE from NOAA

Mention of a commercial company or product does not constitute an endorsement by

NOAA/OAR. Use of information from this publication concerning proprietary products

or the tests of such products for publicity or advertising purposes is not authorized. Any

opinions, findings, and conclusions or recommendations expressed in this material are those

of the authors and do not necessarily reflect the views of the National Oceanic and Atmospheric Administration.

Contribution No. 2985 from NOAA/Pacific Marine Environmental Laboratory

Also available from the National Technical Information Service (NTIS)

(http://www.ntis.gov)

ii
Contents

Abstract 1

1 Background and Objective 1

2 Forecast Methodology 2

2.1 Tsunami Source Based on DART Observations and Tsunami

Source Functions . . . . . . . . . . . . . . . . . . . . . . . . . 4

2.2 Real-Time Site-Specific Forecasting by Stand-by Inundation

Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

3 Developing Forecast Inundation Models for Hawaii 6

3.1 Regional, Coastal, and Nearshore Grids . . . . . . . . . . . . 6

3.2 Sensitivity Study of Site-Specific Inundation Models to Model

Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

3.2.1 Sensitivity of modeled time series to grid resolutions

and computational domains . . . . . . . . . . . . . . . 8

3.2.2 Sensitivity of modeled time series to grid coupling schemes 10

3.2.3 Sensitivity of inundation to topography and friction

coefficients . . . . . . . . . . . . . . . . . . . . . . . . 10

3.3 Procedures and Testing . . . . . . . . . . . . . . . . . . . . . 13

4 Developing a Forecast Inundation Model for Kahului, Hawaii 14

4.1 Study Area and Tsunami Data . . . . . . . . . . . . . . . . . 14

4.2 Bathymetry and Topography . . . . . . . . . . . . . . . . . . 19

4.3 Model Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

4.4 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . 23

4.4.1 Validation and error estimate . . . . . . . . . . . . . . 23

4.4.2 Assessment of potential impact for Kahului from simulated TMw 7.5, 8.2, 8.7, and 9.3 tsunamis . . . . . . . 34

4.4.3 Robustness and stability . . . . . . . . . . . . . . . . . 39

4.4.4 Inundation tests . . . . . . . . . . . . . . . . . . . . . 39

5 Summary and Conclusions 42

6 Acknowledgments 44

7 References 45

List of Figures

1 Computational domain of the propagation database for

the Pacific. . . . . . . . . . . . . . . . . . . . . . . . . . 3

2 Forecast inundation model setups in Hawaii . ..... 7

3 Tsunami time series computed from different grid setups 9

iii
4 Tsunami time series at Hilo tide gage computed from

one- and two-way coupling schemes . . . . . . . . . . . 11

5 Maximum water elevations at Hilo computed from two

sets of topographic and bathymetric grids for the 1946

Unimak tsunami . . . . . . . . . . . . . . . . . . . . . . 12

6 Inundations at Pearl Harbor computed from two sets

of topographic data sources for a simulated TMw 9.3

tsunami . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

7 An aerial photo of Kahului . . . . . . . . . . . . . . . . 16

8 A map of Kahului . . . . . . . . . . . . . . . . . . . . . 17

9 Population density, Maui . . . . . . . . . . . . . . . . . 18

10 Bathymetric and topographic data source overview of

Hawaiian Islands and Maui . . . . . . . . . . . . . . . . 20

11 Grid setup of the Kahului Reference Inundation Model

(RIM) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

12, 1–3 Observed and modeled time series of (a) wave amplitudes and (b, c, and d) wavelet-derived amplitude spectra at Kahului tide gage for the 14 historical tsunamis

in Table 4 . . . . . . . . . . . . . . . . . . . . . . . . . 25

12, 4–6 continued . . . . . . . . . . . . . . . . . . . . . . . . . . 26

12, 7–9 continued . . . . . . . . . . . . . . . . . . . . . . . . . . 27

12, 10–12 continued . . . . . . . . . . . . . . . . . . . . . . . . . . 28

12, 13–14 continued . . . . . . . . . . . . . . . . . . . . . . . . . . 29

13 Comparison and error estimation of (a) maximum wave

height, (b) arrival of the first wave peak, and (c) peak

wave period of observations and model results from the

Kahului SIM. . . . . . . . . . . . . . . . . . . . . . . . . 33

14, 1–7 Maximum water elevation and maximum velocity computed by the Kahului RIM and SIM for the 14 historical

tsunamis. . . . . . . . . . . . . . . . . . . . . . . . . . . 36

14, 8–14 continued . . . . . . . . . . . . . . . . . . . . . . . . . . 37

15 Maximum water elevation at (a) Kahului offshore from

the propagation database and (b, c, d, and e) at Kahului tide station computed by the Kahului SIM for simulated TMw 7.5, 8.2, 8.7, and 9.3 tsunamis . . . . . . . 38

16 Tsunami time series at the Kahului tide station computed by the RIM and SIM from a set of simulated TMw

9.3 earthquakes . . . . . . . . . . . . . . . . . . . . . . 40

17 Maximum water elevation in the study area generated

by the same set of 18 simulated TMw 9.3 tsunamis as

in Fig. 16. . . . . . . . . . . . . . . . . . . . . . . . . . 41

18 Sensitivity of inundation and time series of tsunami amplitudes . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

iv
Contents v

List of Tables

1 Tsunami source functions in the Pacific, Indian, and Atlantic

oceans. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2 Data sources used for grid development. . . . . . . . . . . . . . . 21

3 MOST setup of Kahului RIM and SIM. . . . . . . . . . . . . . . 23

4 Tsunami sources and maximum wave height recorded at Kahului

tide station for 14 historical tsunamis. . . . . . . . . . . . . . . . 31

5 Simulated tsunamis for hazard assessment study for Kahului. . . 35

Developing tsunami forecast inundation models for Hawaii:

Procedures and testing

L. Tang1,2, C. Chamberlin1,2, and V.V. Titov1,2

Abstract. This report describes the procedures and testing for developing tsunami forecast inundation models, named Stand-by Inundation Models (SIMs), for Hawaii, as components of NOAA’s

tsunami forecast and warning system. The activity included sensitivity studies of nearshore tsunami

wave characteristics and inundations for ranges of model grid setups, resolutions, and parameters.

The SIM covering Kahului, Maui, is used as an example for demonstration of the development

process.

The Kahului SIM was validated with 11 historical tsunami water-level records at Kahului tide

station. The accuracy of the maximum wave height computed by the SIM is greater than 80%

when the observed maximum wave height is greater than 0.5 m, and 50% when the observation is

between 0.3 to 0.5 m. The error of the modeled arrival time of the first peak is within ±3% of the

travel time. Wavelet analyses indicate that the peak wave period at the station mainly falls into

one of three harbor and local resonant periods, near 16, 24, or 34 min (±2 min). This is relevant

to the geographic location of the tsunami source. The SIM outputs are also verified with numerical

results from a reference inundation model (RIM) with a higher resolution of 1/3 arc-second (10 m).

The optimized SIM can accurately provide a 4-hour forecast of first-wave arrival, amplitudes, and

a reasonable inundation limit within minutes of receiving tsunami source information constrained

by deep-ocean DART measurements. It is capable of reproducing later tsunami waves reflected

or scattered by far-field bathymetry that may arrive hours after the first arrival. The Kahului

SIM is tested against different scenarios of simulated TMw 7.5, 8.2, 8.7, and 9.3 tsunamis based on

subduction zone earthquakes in the Pacific. It shows robust results for all test cases.

The tsunami hazard assessment study for Kahului indicates that moment magnitude alone is inadequate to provide warning guidance for coastal communities, since it contains information relevant

only to the source. The SIMs, which contain local bathymetric and topographic information, and

utilize the dynamic boundary conditions from the propagation database, are particularly designed

for site-specific forecasts for coastal communities. Only by combining DART-constrained tsunami

magnitude with site-specific SIMs can the forecast completely cover the three distinct stages of

earthquake-generated tsunamis—generation, deep-ocean propagation, and coastal transformation,

including runup.

1. Background and Objective

The NOAA Center for Tsunami Research (NCTR) at NOAA’s Pacific Marine Environmental Laboratory (PMEL) is developing a tsunami forecasting

system known as Short-term Inundation Forecasting for Tsunamis (SIFT)

for NOAA’s Tsunami Warning Centers (Titov et al., 2005). The primary

goal of the system is to provide NOAA’s Tsunami Warning Centers with

operational tools that combine real-time deep-ocean tsunami measurements

from the Deep-ocean Assessment and Reporting of Tsunami (DART) buoys

(Gonz ́alez et al., 2005; Bernard et al., 2006; Bernard and Titov, 2007), with

the Method of Splitting Tsunami (MOST) model, a suite of finite difference numerical codes based on nonlinear long wave approximation (Titov

1Joint Institute for the Study of the Atmosphere and Ocean, University of Washington,

Seattle, WA 2NOAA, Pacific Marine Environmental Laboratory, Seattle, WA
2 Tang et al.

and Synolakis, 1998; Titov and Gonz ́alez, 1997; Synolakis et al., 2007), to

produce efficient forecasts of tsunami arrival time, heights, periods, and inundation. To achieve accurate and detailed forecasts on the likely impact of

incoming tsunamis on specific sites within certain time limits and to reduce

false alarms, Stand-by Inundation Models (SIMs) are being developed for

U.S. coastal communities that are potentially most at risk, and integrated

as crucial components of the forecast system.

Presently, a system of 35 DART buoys (32 U.S.-, 1 Chilean-, and 2

Australian-owned) is monitoring tsunami activity in the Pacific Ocean

(Fig. 1) (44 DART buoys globally). The pre-computed propagation models

currently have 899 scenarios to cover Pacific tsunami sources (1299 globally), and the high-resolution forecast inundation models (SIMs) are now set

up for 26 U.S. coastal communities. The fully implemented system will use

real-time data from the DART network to provide high-resolution tsunami

forecasts for at least 75 communities in the U.S. (by 2013) (Titov, 2008).

Since its first testing in the 17 November 2003 Rat Island tsunami, the forecast system has produced experimental real-time forecasts for eight tsunamis

in the Pacific and Indian oceans (Titov et al., 2005; Wei et al., 2008; Titov,

2008). The forecast methodology has also been tested with the data from

nine additional events that produced the deep ocean data.

The present study standardizes procedures and testing for developing

real-time forecast inundation models (SIMs) for Hawaii based on sensitivity

studies. A detailed SIM development is presented for Kahului, Hawaii. This

study also performs tsunami hazard assessment and identifies worst-case scenarios from major subduction zone earthquakes that may have a devastating

impact on the study site. A secondary objective is to investigate Kahului

harbor and local responses to tsunami waves by wavelet analysis.

The remainder of this report is organized as follows. Section 2 introduces PMEL’s tsunami forecast methodology. Section 3 describes coastal

and nearshore segment setups for the Hawaiian region, discusses the problems and difficulties encountered during SIM developments in the past, and

standardizes the procedures and testing for developing forecast inundation

models for Hawaii. A detailed SIM development for Kahului is provided

in section 4, including validation, testing for robustness and stability, and

hazard assessment. A summary and conclusions are presented in section 5.

2. Forecast Methodology

PMEL’s real-time tsunami forecasting scheme is a two-step process: (1)

constructing a tsunami source through inversion of deep ocean DART observations utilizing pre-computed tsunami source functions, and (2) realtime site-specific forecasting for coastal communities by SIMs, where MOST

operates differently (Titov et al., 1999; 2005).
Tsunami forecast inundation models for Hawaii

3Figure 1: Computational domain of the propagation database for the Pacific.
4 Tang et al.

2.1 Tsunami Source Based on DART Observations and

Tsunami Source Functions

A tsunami source refers to an equivalent earthquake that is able to reproduce

similar tsunami wave characteristics, including arrival, height, and period,

in the deep ocean without knowing details of the earthquake’s focal mechanism. The wave dynamics of tsunami propagation in the deep ocean can be

approximated using linear theory. Thus a tsunami source can be effectively

constructed based on the best fit to given deep-ocean tsunami measurements

with pre-computed tsunami source functions.

Titov et al. (1999; 2001) conducted sensitivity studies on far-field deepwater tsunamis based on various parameters of commonly used fault plane

source models (Gusiakov, 1978; Okada, 1985). The results showed that

source magnitude and location essentially define far-field tsunami signals

for a wide range of subduction zone earthquakes. Other parameters have

a secondary influence and can be ignored during forecast. Based on the

results, propagation databases for the Pacific, Atlantic, and Indian oceans

have been built using pre-defined source parameters: length = 100 km, width

= 50 km, slip = 1 m, rake = 90 and rigidity = 4.5 × 1010 N/m2. Other

parameters are location specific. (Details of the databases are described in

Gica et al., 2008.) Each scenario represents a tsunami from a typical Mw

= 7.5 earthquake and we refer to it as one tsunami source function (TSF).

Figure 1 shows the earthquake locations of tsunami source functions and

Table 1 summarizes the databases. Presently, the Pacific database contains

899 TSFs (1299 globally). At each subduction zone, up to five lines of TSFs

from seaward to landward, B, A, Z, Y, and X, are placed adjacent to one

another. Figure 1 also shows the computational domain of the database in

the Pacific, the propagation grid for MOST, which extends from 120◦E 70◦S

to 68◦W 62◦N, with a resolution of 4 min and a time step of 15 sec. The

computational results, including amplitudes and depth-averaged velocities,

were saved in the database at every 16 min in space and 60 sec in time.

Several real-time data sources, including seismic, coastal tide gage, and

deep-ocean data have been used for tsunami warning and forecast. PMEL’s

strategy for real-time forecasting is to use deep-ocean measurements at

DART buoys as the primary data source based on several key features: (1)

They are the direct measure of tsunami waves, unlike seismic data, which

are indirect. (2) Compared with coastal tide gages, DART data of high

signal-to-noise ratio can be obtained quickly without harbor and instrument

responses. (3) The linear process of tsunamis in the deep ocean allows the

application of efficient inversion schemes.

Time series of tsunami observations in the deep ocean can be decomposed into a linear combination of a set of tsunami source functions in the

time domain by the linear least squares method. We refer to the coefficients

obtained through this inversion process as tsunami source coefficients. And

the magnitude computed from the sum of the magnitudes of TSFs multiplied by the corresponding coefficients is referred to as the tsunami moment

magnitude (TMw), to distinguish it from the seismic moment magnitude
Tsunami forecast inundation models for Hawaii 5

Table 1: Tsunami source functions in the Pacific, Indian, and Atlantic oceans.

Subduction Zone Tsunami Source Functions

No. Abbr. Name Line/Zone Numbers

1 AACC Aleutian-Alaska-Canada-Cascadia BAZYX 162

2 CASZ Central American BA 72

3 CESZ Columbia-Ecuador BA 36

4 EPSZ East Philippines BA 38

5 KKJI Kamchatka-Kuril-Japan Trench-Izu Bonin-Marianas-Yap BAZY 184

6 MOCB Manus Ocean Convergence Boundary BA 34

7 NBSV New Britain-Solomons-Vanuatu BA 74

8 NNGZ North New Guinea BA 30

9 NZKT New Zealand-Kermadec-Tonga BA 78

10 RKNZ Ryukus-Kyushu-Nankai BA 44

11 SASZ South American BAZY 103

12 SCSZ South Chile BA 30

13 NZSZ South New Zealand BA 14

Subtotal: 899

14 ATSZ Atlantic BA 184

15 ANSJ Adaman-Nicobar-Sumatra-Java BAZY 174

16 MKSZ Makran BA 20

17 WPSZ West Philippines BA 22

Total: 1299

Mw, which is obtained from the moment tensor analysis of seismic waves.

The inversion process uses tsunami travel time to locate the source and the

observed tsunami amplitudes to constrain the magnitude. Wave period is

mainly defined by source location.

The database can provide an offshore forecast of tsunami amplitudes

and all other wave parameters around the Pacific immediately once the inversion is complete. The tsunami source, which combines real-time tsunami

measurements with TSFs, provides an accurate offshore tsunami scenario

without additional time-consuming model runs.

2.2 Real-Time Site-Specific Forecasting by Stand-by

Inundation Models

The evolution of earthquake-generated tsunami waves has three distinctive stages: generation, propagation, and coastal transformation, including

runup. The SIM is particularly designed for the last stage, which is very

important since it provides information on the likely impact of an incoming

tsunami on site-specific coastal communities, where lives and properties are

at risk. The DART-constrained tsunami source, the corresponding offshore

scenario from the propagation database, and the site-specific SIMs cover all

three stages, providing a complete tsunami forecast capability.

Tsunami inundation is a highly nonlinear process. Forecasting of the

maximum wave height nearshore also requires non-linear inundation models and fine-resolution bathymetry/topographic data. The SIM utilizes the

rigorously tested Method of Splitting Tsunami (MOST) model, a finite dif-
6 Tang et al.

ference tsunami inundation model based on nonlinear shallow-water wave

equations. Each SIM consists of three telescoping computational grids for

regional, coastal, and nearshore areas, with increasing resolution. Runup

and inundation are computed within the nearshore grid. The nearshore

grid includes the population center and tide stations for forecast verification. The computational grids for SIMs are derived from the best available

bathymetry/topographic data at the time of development. Grids will be continuously updated when better bathymetry/topographic data is available.

SIMs are implemented and optimized for speed and accuracy. Once

the tsunami source is obtained, the pre-computed time series of offshore

wave height and depth-averaged velocity in the propagation database are

applied as the dynamic boundary conditions for SIMs, which saves additional

computational time for propagation. By reducing the computational areas

and grid resolutions, which allows larger time steps without violations of

the CFL conditions, SIMs are optimized to provide 4-hour event forecasting

results in minutes of computational time using a single processor. To ensure

forecast accuracy, SIM outputs are validated and verified with historical

tsunami records as well as results from a reference inundation model (RIM)

with higher resolutions and extended computational domains. In order to

provide warning guidance for a long duration during a tsunami event, each

SIM has been tested to output a simulation for up to 24 hours after the

tsunami generation.

3. Developing Forecast Inundation Models

for Hawaii

3.1 Regional, Coastal, and Nearshore Grids

The forecast setup for Hawaii consists of three layers of telescoping grids as

shown in Fig. 2.

(a) One regional grid of 2-arc-min resolution covers the main Hawaiian Islands.

(b) The whole Hawaiian coastline is divided into four coastal grids of 12- to

18-arc-sec for four natural geographic groups:

(b.1) Ni‘ihau, Ka‘ula Rock, and Kauai (Kauai complex)

(b.2) Oahu,

(b.3) Molokai, Maui, Lanai, and Kaho‘olawe (the Maui Complex), and

(b.4) Hawaii.

(c) Within each coastal grid, the coastline is further divided into 2-arcsec nearshore grids. Runup and inundation are computed within the

nearshore grids, where it has a high concentration of population or

activities.
Tsunami forecast inundation models for Hawaii 7

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19.7619.71

HAWAIIAN ISLANDS 

Kauai 

Niihau 

Oahu

Maui

Hawaii 

Molokai

Lanai

Kahoolawe

Nawiliwili 

Honolulu 

Kahului Hilo 

(a.1)

(b.1) (b.2) (b.3) (b.4)(c.1) (c.2) (c.3) (c.4)

Figure 2: Forecast inundation model setups in Hawaii: (a) regional, (b) coastal, and (c) nearshore grids.
8 Tang et al.

At present, each SIM is independently set up to use three telescoping

rectangular grids. NCTR has ongoing research on implementation of the

MOST model with curvilinear and multi-nesting grids. SIMs can be set up

to utilize the shared regional or coastal grids to improve forecast speed in

the future.

3.2 Sensitivity Study of Site-Specific Inundation Models to

Model Setup

How sensitive are the model outputs, including time series and inundation, to changes in the grid resolutions, computational domains, accuracy

of bathymetry/topography, and other parameters? This issue is central to

SIM development, since giving a correct tsunami source and a well-validated

tsunami inundation numerical model, with an inappropriate model setup or

inaccurate bathymetry/topography, can produce poor results.

3.2.1 Sensitivity of modeled time series to grid resolutions and

computational domains

Figure 3 compares results from different model setups for Kahului, Honolulu, and Los Angeles. Setup 3 has resolutions of 120, 24, and 3 for the

Kahului regional, coastal, and nearshore grids (Fig. 3a). The observed maximum wave amplitude is 25 cm during the 2006 Tonga tsunami, while the

modeled maximum amplitude in setup 3 is only 11 cm (−56% error). With

a higher resolution of 12 and an extended computational domain applied

to the coastal grid, which includes portions of nearby Molokai, Lanai, and

Kaho‘olawe islands, setup 2 produces a 21-cm maximum amplitude. For a

4-hour simulation, the computational time increases from about 8 min for

setup 3 to 10 min for setup 2. Further increasing grid resolutions to 36,

6, and 1 as in setup 1 produces a 28-cm maximum amplitude. Meanwhile

the computational time increases to about 8 hours. Prior to the 2006 Tonga

tsunami, setup 3 was tested with six historical events, the 2003 Rat Island,

2003 Hokkaido, 1996 Andreanof, 1994 East Kuril Island, 1964 Alaska, and

1957 Andeanof tsunamis. It produced good comparisons to the observations

at the Kahului tide station. However, when the 2006 Tonga tsunami came

from a direction from which neither data exists nor a test had been done

before, the hidden deficiency of setup 3 was exposed. Therefore, to ensure

the computational domains for SIMs, including the appropriate bathymetry

features, and as a consequence, to provide the right boundary conditions

for modeling of wave scattering, it is important to test Hawaiian SIMs with

tsunamis from all potential directionalities.

In Fig. 3b, grid setup 2 of finer resolution for Honolulu shows a better

comparison of wave height and phase for later waves than those of setup 3

for the 1964 Alaska tsunami. While it takes less than 10 min for a 4-hour

simulation for setups 2 and 3, it takes about 64 hours for the finest grid

setup 1. The finer the resolution, the better the detail of the fine structures

of Honolulu harbor.
Tsunami forecast inundation models for Hawaii 9

6 6.25 6.5 6.75 7 7.25 7.5 7.75 8 8.25 8.5 8.75 9 9.25 9.5 9.75 10 10.25 10.5 10.75 11 −0.4

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 (a) Kahului Tide Gage 2006.05.03 15:26:39 UTC Tonga Tsunami NZKT 

Amplitude (m) 

Time (hour) 

( Continued )

Obs.

Setup 1: 36", 6", 1"

Setup 2: 120", 12", 3"

Setup 3: 120", 24", 3"

4 4.25 4.5 4.75 5 5.25 5.5 5.75 6 6.25 6.5 6.75 7 7.25 7.5 7.75 8 8.25 8.5 8.75 9 9.25 9.5 9.75 10

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 (b) Honululu Tide Gage 1964.03.28 03:36 Alaska Tsunami AACC 

Obs.

Setup 1: 36", 6",1/3"

Setup 2: 120", 18", 2"

Setup 3: 120", 24", 3"

8 8.5 9 9.5 10 10.5 11 11.5 12 12.5 13 13.5 14 14.5 15 15.5 16 16.5 17 17.5 18

−0.1

−0.05

0

0.05

0.1

Time (hour) 

Amplitude (m) 

 (c) Los Angeles Tide Gage 2006.05.03 15:26:39 UTC Tonga Tsunami NZKT 

Obs.

Setup 1: 32.1 to 34.9 deg N

Setup 2: 29.0 to 36.0 deg N

Figure 3: Tsunami time series computed from different grid setups at (a) Kahului tide gage for the 2006

Tonga tsunami, (b) Honolulu tide gage for the 1964 Alaska tsunami, and (c) Los Angeles tide gage for the

2006 Tonga tsunami.
10 Tang et al.

Figure 3c presents an 8-min difference in the arrival time of the first peak

from two model time series at Los Angeles tide station for the 2006 Tonga

tsunami. The 2-arc-min offshore grid for setup 2 was further extended to the

south of Los Angeles to include some shallow bathymetric features. It produces better agreement with the observations when the tsunami propagates

from the southwest.

Forecast inundation models need to balance between speed and accuracy.

One important guideline in developing tsunami forecast models is to remain

within acceptable time limits, using the highest resolution and largest computational domains possible.

3.2.2 Sensitivity of modeled time series to grid coupling schemes

MOST version 1.0 employs a two-way coupling scheme. The coupling is

achieved at each time step in the same way that coarse-to-fine resolution

level boundary conditions are interpolated from the low-resolution field, and

vice versa. The two-way coupling scheme has relatively rigorous requirements for bathymetric consistency as well as time steps between adjacent

grids. One example is that water depth at the same location offshore of north

Oahu differs by 400 m at 2000-m water depth from two different bathymetric

data sources. These two sources were applied to construct the regional and

coastal grids, respectively, for Honolulu. With the northern boundary in the

coastal grid lying through such sudden changes of water depth, boundary

instabilities were developed right from the beginning of the model run. Furthermore, even with a consistent bathymetric data source, time steps for the

three telescoping grids still need to be carefully tested in order to provide

stable model runs of long duration. To overcome these difficulties, a oneway coupling scheme was employed in MOST version 2.0, e.g., there was no

interpolation of the fine-resolution field to the coarser resolution level, for

forecast purposes. The one-way coupling scheme is robust and can handle

bathymetric grids from varieties of data sources with any time steps that

satisfy CFL conditions. MOST version 2.0 passed the bench mark tests and

in general provided good comparisons with model results from version 1.0.

However, there is one exception: so far, we have seen that one-way coupling

overestimates the amplitude of the 3rd trough and the 4th peak at Hilo tide

station for two events, the 2006 Kuril Islands and 2003 Rat Island tsunamis

(Fig. 4). The reason is still under investigation. We suggest double checking

forecast results for the Hilo SIM by using the two-way coupling scheme.

3.2.3 Sensitivity of inundation to topography and friction coefficients

Accurate simulation of tsunami run-up and inundation requires high quality run-up and inundation data, high-resolution bathymetry and topography

data in the runup area, and good tsunami source parameters. Titov et al.

(2005) have shown that, under these conditions, the MOST runup and inundation agree quite well with the stereo aerial photo data and filed survey data

on Okushiri Island from the 12 July 1993 Hokkaido-Nansei-Oki Mw = 7.8

earthquake.
Tsunami forecast inundation models for Hawaii 11

4 4.25 4.5 4.75 5 5.25 5.5 5.75 6 6.25 6.5 6.75 7 7.25 7.5 7.75 8 8.25 8.5 8.75 9 −0.5

−0.4

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−0.2

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0

0.1

0.2

0.3

0.4

0.5

Time (hour) 

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( b ) Hilo Tide Gage 2003.11.17 06:43 Rat Island Tsunami AACC ( Forecast tsunami source )

1 2 3 4 5 6 7 8 9 10 11

Obs.

One−way

Two−way

6 6.25 6.5 6.75 7 7.25 7.5 7.75 8 8.25 8.5 8.75 9 9.25 9.5 9.75 10 10.25 10.5 10.75 11 −1

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( a ) Hilo Tide Gage 2006.11.15 11:14:17 UTC Central Kurile Is Tsunami KKJT ( Forecast tsunami source )

1 2 3 4 5 6 7 8 9 10 11

Obs.

One−way

Two−way

Figure 4: Tsunami time series at Hilo tide gage computed from one- and two-way coupling schemes for (a)

the 2006 Kuril Islands tsunami and (b) the 2003 Rat Island tsunami.

At present, one major difficulty in inundation forecasting is lack of highquality inundation/runup measurements to verify the topographic accuracy

and to calibrate the friction coefficient.

Topography/bathymetry compiled with incorrectly aligned datum or from

different data sources can produce different inundation results. Figures 5a

and 5b show the inundation computed from two sets of grids with the same

nearshore 2-arc-sec resolution at Hilo for the 1946 Unimak tsunami. Grid

2 correctly reproduced the inundation limit as shown in Fig. 5c, while no

inundation was produced in Grid 1 (Fig. 5a). The topographic 0-, 2-, 5-,

and 10-m contours are quite different between these two grids. Developed

in 2006 for the Hilo SIM, all data sources for Grid 2 were converted to WGS

84 horizontal geodetic datum and mean high water vertical datum, when

necessary. Whether or not the data sources in Grid 1 were converted to the

same datum was unclear.

Figures 6a and 6b show that two topographic data sources produced different inundation results along the coastline from Ewa Beach to the Pearl

Harbor entrance from a simulated TMw 9.3 tsunami on the Solomon subduction zone near Santa Cruz Islands. Both nearshore grids have 1/3-arcsec (10-m) resolution. The high-resolution recent topographic LIDAR from

NOAA Coastal Service Center was applied in Grid 2, which was derived for
12 Tang et al.

Map of the Hilo area, Hawaii, showing the heights reached by the water, the area of flooding, and the sections of breakwater destroyed, during

the tsunami of April 1, 1946. Heights are in feet above lower low water. 

(c)

0 m contour

Modeled inundation limit

Figure 5: (a) and (b) Maximum water elevations at Hilo computed from two sets of topographic and

bathymetric grids for the 1946 Unimak tsunami. (c) Comparison between computed inundation in (b) and

measurements from Shepard et al. (1950).
Tsunami forecast inundation models for Hawaii 13

Figure 6: Inundations at Pearl Harbor computed from two sets of topographic data sources for a simulated

TMw 9.3 tsunami. Topography in (a) was derived from USGS DEM and (b) from CSC LIDAR data. Color

represents the maximum water elevation in meters.

the tsunami hazard assessment study for Pearl Harbor (Tang et al., 2006).

The LIDAR data has a “tested 16.9 cm fundamental vertical accuracy at 95

percent confidence level in open terrain,” with nominal Ground spacing of

2m(http://maps.csc.noaa.gov). The data was processed to bald earth

and interpolated to a 10-m gridded data. The topographic data for Grid 1

was derived from the USGS 7.5-min DEM based on 30-m data spacing. The

major 2-, 5-, and 10-m contours agree reasonably well for these two data

sets. However, the shore LIDAR data show a long narrow dune with an

elevation around 2 m along Ewa Beach, which is absent in the USGS DEM.

This results in the difference in inundation seen in Fig. 6. A coastline with

long narrow dunes is a common feature in the Hawaiian Islands. Attention

must be paid to such features during SIM development. Details of the data

sources for Grid 2 can be found in Tang et al. (2006).

As will be discussed in Section 4.4.4, a small Manning coefficient such as

n = 0.01 can produce further inundation at certain flat areas for some test

cases.

3.3 Procedures and Testing

The sensitivity study in the previous section provides lessons and guidance

for developing site-specific tsunami forecast inundation models. The studies

demonstrate that for a fixed tsunami source and a well-validated numerical

tsunami inundation model:

(1) Model setups, including grid resolutions and computational domains,

are the key factors in accurately modeling the maximum wave height

and arrival time nearshore. Other factors, such as tsunami directionalities and grid coupling schemes, may have effects on certain sites for

certain events.

(2) Inundation is strongly dependent on the accuracy and spatial resolution

of the topography. A small friction coefficient may produce further

inundation at some flat areas for some test cases.
14 Tang et al.

Based on the above results, procedures and testing for SIM development

are suggested as followed:

(1) Bathymetry and topography. Derive DEMs from the best available

bathymetric and topographic data sources at the time of development.

Update DEMs when a better source is available.

(2) Resolutions and computational domains. Within acceptable computational time limits, apply the highest resolutions and largest computational domains for the SIM. Develop a Reference Inundation Model

(RIM) of higher resolutions and extended computational domains for

each SIM to provide numerical references for the SIM. Include bathymetric and topographic features within or close to the forecast site

in the computational domains, such as nearby islands or long narrow

dunes along coastlines, to provide correct coastal boundary conditions.

(3) Validation and verifications. Validate and verify both the SIM and RIM

with all available historical tsunami data, including tide gage records

and inundation/runup measurements. Coastal tide gage data are available for Hawaii from fourteen tsunamis since 1946 (Table 4). Test the

sensitivity of inundation to a range of friction coefficients.

(4) Robustness and stability. Test the SIM and RIM with different scenarios

of simulated tsunamis based on major subduction zone earthquakes

from all possible directionalities relative to the main Hawaiian Islands.

Verify the SIM results with those of the RIM to ensure robustness. Test

the SIM for stability up to 24-hour model runs for both historical and

simulated scenarios of great subduction zone tsunamis.

A detailed SIM development for Kahului following the above procedures is

described in the next section.

4. Developing a Forecast Inundation

Model for Kahului, Hawaii

4.1 Study Area and Tsunami Data

The main Hawaiian Islands are the younger and southern portion of the

Hawaii Archipelago. From northwest to southeast, the islands form four

natural geographic groups by shared channels and an inter-island shelf, including (1) Ni‘ihau, Ka‘ula Rock, and Kauai (Kauai complex) (2) Oahu, (3)

Molokai, Maui, Lanai, and Kaho‘olawe (the Maui Complex), and (4) Hawaii.

Kahului is located at the north shore of Central Maui and is the largest town

on Maui. It hosts Maui’s main airport, Kahului Airport, deep-draft harbor,

Kahului Harbor, light industrial areas, and commercial shopping centers.

Figure 7 presents an aerial photo of this area and a map is shown in Fig. 8.

The population density data in Fig. 9 indicates a high concentration of population in Kahului.
Tsunami forecast inundation models for Hawaii 15

The coastal geological features around the Island of Maui are complex.

Maui is surrounded to the northwest, west, and south by three smaller islands nearby, Molokai, Lanai, and Kahoolawe, with three channels in between (Fig. 11b). These three channels, Pailolo Channel, Auau Channel,

and Alalakeiki Channel have narrow widths of 12.9 km (8 miles), 15 km (9.2

miles), and 11 km (7 miles), respectively. Most portions of the channels

are quite shallow, with water depth of less than 300 m. Certain sections

of the Auau Channel, which connects Maui and Lanai, are less than 50 m

deep. To the southeast, the 48-km-wide (26-mile), 2-km-deep Alenuihaha

Channel separates Maui from the Big Island of Hawaii. The island of Maui

is unprotected against waves from north and northeast.

The Kahului nearshore is gently embayed, with an average slope of 0.016

from the 0-m down to the 500-m depth contour. On the land, a narrow flat isthmus unites Maui’s dominant geological features, two volcanoes,

Haleakala (on eastern Maui) and the West Maui Mountains. The isthmus is

11 km (7 miles) across, with the highest elevation of less than 40 m. Other

portions of the northern coast of Maui consists generally of cliffs. Coral reefs

in shallow water of 1 to 3 feet are as much as 1.2 miles (1.8 km) wide in

the study area. The study area covers the coastal communities of Kahului,

Wailuku, and Waiehu along the north shore of central Maui, Hawaii. The

location of the Kahului tide station is chosen as the warning point (Fig. 8).

Established 19 December 1946 in Kahului Harbor, Kahului tide station

has provided valuable records of historical tsunamis. A gas-purging pressure tide gage, also known as the bubbler gage, was installed in 1946. The

data was initially recorded on a pen and ink strip chart (Little, 2006). In

the mid-1970s this equipment was replaced with an ADR (Analog to Digital

Recorder) that used a digital paper punch and recorded the height of water

level at 6-min intervals. In February 1989, the Kahului gage was replaced

with the Next Generation Water Level Measurement System (NGWLMS).

The new primary water-level sensor is an air acoustic measurement device.

It is both self-calibrating for variations in the speed of sound, and can be

leveled directly to a local benchmark that provides absolute measurements

referenced to the local water-level datum. It employs a less restrictive protective well with parallel plates, which only screens out waves with a period

shorter than 2–3 sec. The new system’s data sampling procedures in conjunction with the open protective well is a significant improvement over the old

one (NOAA/NOS, 1991). In 2005, the Kahului tide station was upgraded

to one of the tsunami-capable tide stations by NOS/CO-OPS, with new

hardware and software to enable the collection and dissemination of 1-min

water-level sample data (http://tidesandcurrents.noaa.gov/1mindata.

shtml). The stations also sample 15-sec data, which can be downloaded

later. The MHW at the Kahului tide station is 1.313 m and the MSL is

1.075 m (http://tidesandcurrents.noaa.gov/). The mean range of tide

is 0.478 m.

Kahului has a long history of destructive tsunamis. The earliest record

of a destructive tsunami at Kahului was on 7 November 1837, when the sea

first receded horizontally 36 m and then a wall of returning water generated

by a wave from southern Chile engulfed inhabitants who were collecting
16 Tang et al. Figure 7: An aerial photo of Kahului (http://www.soest.hawaii.edu/coasts/).
Tsunami forecast inundation models for Hawaii 17 Figure 8: A map of Kahului. Inset: Red circle, Kahului tide gage (the warning point).
18 Tang et al.

Hana

Pa'ia

Kihei

Kahana

Kahului

Lahaina

Population density

km

(persons/km2)

<4000

4000–8000

8000–20000

>20000

Inundation model extent

0 5 10 20

Figure 9: Population density, Maui (Source: 2000 Census).

stranded fish (Pararas-Carayannis, 1969). Two people were drowned and

the rest swam to safety. Twenty-six grass houses were carried about 240 m

inland. Since 1813, 54 tsunamis have been observed in Kahului, including

23 tsunamis during the period of 1813 to 1968 (a total of 85 tsunamis were

observed in the Hawaiian Islands during this period, but unfortunately many

of them have no record for Kahului) (Pararas-Carayannis, 1969), 11 between

1969–1982 (Soloviev et al., 1992), 3 during 1983 to 1991, and at least 17 from

1992 to the present. Many of them caused significant damage.

The 3 February 1923 East Kamchatka tsunami caused “heavy damage in

Kahului and east coast of Maui.” The 1 April 1946 Unimak Island tsunami

has the highest tsunami run-up records in the study area among the tsunamis

in Table 4. Coral blocks as large as 4 feet in diameter were thrown on shore

just east of the breakwater (Shepard et al., 1950). At Spreckelsville the wave

reached an elevation of 28 feet and swept inland as far as 800 feet. After

that, Kahului tide gage was installed at the northwest corner of pier 2 in

Kahului Harbor. “The Kahului-Spreckelsville region suffered the greatest

damage” from the 4 November 1952 tsunami from East Kamchatka. On 9

March 1957, the Andreanof tsunami event exceeded the Kahului gage limit

of 1.7 m, resulting in considerable damage along the northeast of the Island

of Maui (Salsman, 1959). The maximum wave height of the 22 May 1960

South Chile tsunami exceeded the Kahului gage limit of 2.8 m. On 28 March
Tsunami forecast inundation models for Hawaii 19

1964, the gage recorded a maximum wave height of 3.35 m (peak to trough)

during the Alaska tsunami. The shopping center near the waterfront was

flooded and the total damage was $52,590 in Kahului (Pararas-Carayannis,

1969).

As a population center that has been repeatedly affected by Pacific

tsunamis, Kahului is in need of a stand-by inundation model for tsunami

forecasting to aid site-specific evacuation decisions.

4.2 Bathymetry and Topography

Tsunami inundation modeling requires accurate bathymetry in coastal areas as well as high-resolution topography and bathymetry in nearshore areas.

Two gridded digital elevation models (DEMs) were developed, a bathymetric DEM at medium resolution (6 arc-sec) for wave transformation from

the open ocean to coastal areas; and a high resolution (1/3 arc-sec) topography and bathymetry DEM for modeling wave runup and inundation

onto dry land. The grids were compiled from several data sources; Fig. 10

is an overview of the spatial extents of each data source used. In areas

where multiple datasets overlapped, higher-resolution and newer datasets

were generally preferred, and superseded datasets were used for comparison

and verification. Table 2 is an overview of the data sources used; in general,

the data sources listed first superseded data sources listed later when they

overlapped.

Source details for the datasets incorporated into the model grids:

• Joint Airborne Lidar Bathymetry Technical Center of Expertise

(JALBTCX), U.S. Army Corps of Engineers, Mobile District. Online reference: http://shoals.sam.usace.army.mil/hawaii/pages/

Hawaii_Data.htm.

• Monterey Bay Aquarium Research Institute (MBARI) Hawaii Multibeam Survey, Version 1. Online reference: http://www.mbari.org/

data/mapping/hawaii/.

• USGS Pacific Seafloor Mapping Project. Online reference: http://

walrus.wr.usgs.gov/pacmaps/data.html.

• Japan Agency for Marine-Earth Science and Technology (JAMSTEC)

1998–1999 multibeam bathymetric surveys. Published in: Takahashi,

E. et al. (eds.) (2002): Hawaiian Volcanoes: Deep Underwater Perspectives. American Geophysical Union Monograph 128.

JAMSTEC trackline data was recorded by the R/V Mirai during transits in 1999 and 2002. Online reference: http://www.jamstec.go.jp/

mirai/index_eng.html.

• United States Army Corps of Engineers (USACE), Honolulu District.

Online reference: http://www.poh.usace.army.mil/.

• NOAA National Geophysical Data Center (NGDC). Online reference:

http://www.ngdc.noaa.gov/mgg/gdas/gd_sys.html.

• NOAA National Ocean Service (NOS). Sounding points were digitized

from NOS nautical charts 19347, 19358, 19359, 19364, 19366, 19342,
20 Tang et al.

SHOALS LIDAR

JAMSTEC multibeam

MBARI multibeam

Navy multibeam

NOS digital echosounder

NOS multibeam

NOS lead-line surveys

USACE digital echosounder

USGS Seafloor Mapping Project multibeam

NOS nautical chart digitized contours

USGS GLORIA tracklines/Smith and Sandwell

NOAA CSC IfSAR topography

USGS National Elevation Dataset topography

Maui

Kahului

Kihei

(a)

(b)

Figure 10: Bathymetric and topographic data source overview. (a) Hawaiian Islands with 6-arc-sec resolution; (b) Maui with 1/3-arc-sec resolution.
Tsunami forecast inundation models for Hawaii 21

Table 2: Data sources used for grid development.

Data Provider Data Type Survey Dates Description

Joint Airborne Lidar Bathymetry

Technical Center of Excellence

(JALBTCX)

Points 1999–2000 Nearshore bathymetry and topography

from SHOALS airborne LIDAR. 1–5-

m horizontal resolution.

Monterey Bay Aquarium Research

Institute (MBARI)

Grid 1998 Multibeam bathymetric surveys. 10–

30-m horizontal resolution.

USGS Pacific Seafloor Mapping

Project

Grid 1998 Multibeam bathymetric surveys. 8-m

resolution

Japan Agency for Marine-Earth Science and Technology (JAMSTEC)Grid 1998–2002 Multibeam bathymetric surveys. 150-

m horizontal resolution. Multibeam

tracklines at varying resolutions.

United States Navy Point 2000 Multibeam surveys, south and west

sides of Oahu

United States Army Corps of Engineers, Honolulu District (USACE)Point 2000–2005 Digital echosounder surveys in USACE

harbor project areas

National Geophysical Data Center

(NGDC)

Point 1968–1992 Bathymetric survey data. Multiple

technologies, including lead line, digital echosounder, and multibeam.

National Ocean Service (NOS) Point 1979–1989, 2005 Older bathymetric data points digitized

from NOS nautical charts. Recent

points imported from Electronic Navigational Charts (ENCs).

Smith and Sandwell (1997) Point 1997 2-min resolution bathymetry derived

from satellite altimetry and ship

tracklines.

USGS Geological Long-Range Inclined Asdic (GLORIA)Point 1986–1988 Sidescan sonar bathymetric surveys in

deep-water regions of Hawaii’s EEZ.

NOAA Coastal Services Center Grid 2005 IfSAR (radar altimetry) topographic

survey. Gridded to 5-m horizontal resolution.

USGS National Elevation Dataset Grid Varies 10-m resolution topographic data derived from USGS DEMs

19381, and 19324. Sounding data from electronic chart (ENC) 19357

was used. This data was included in relatively shallow regions where

other data sources were sparse or unavailable, or for quality control of

other sources.

• Smith, W.H.F., and D.T. Sandwell, Global seafloor topography from

satellite altimetry and ship depth soundings, Science, 277, 1957–1962,

26 September 1997. Online reference: http://topex.ucsd.edu/WWW_

html/mar_topo.html.

• USGS Geological Long-Range Inclined Asdic (GLORIA) surveys. Online data reference: http://walrus.wr.usgs.gov/infobank/ .

• NOAA Coastal Services Center. http://www.csc.noaa.gov/. The

IfSAR topographic data was collected and processed for CSC by Intermap Technologies Inc. The data is subject to a restrictive license

agreement and is not publicly available.

• USGS National Elevation Dataset. Online reference: http://seamless.

usgs.gov/ .
22 Tang et al.

The SHOALS LIDAR project, which provides high-resolution unified topographic and bathymetric data for the nearshore areas of several Hawaiian

Islands, including all of Maui, was essential for accurate modeling of reef

and intertidal regions where conventional bathymetric survey data is usually coarse or unavailable. Quality data in this region is especially essential because bathymetric inaccuracies have a great impact on tsunami wave

dynamics in shallow water. The 2005 NOAA CSC IfSAR survey of Maui

provided similarly valuable high-resolution topography for the entire island,

enabling greater confidence in predicting inundation extents. The USGS

National Elevation Dataset (NED) was used on other islands outside of the

primary study area.

High-resolution gridded datasets derived from multibeam surveys are

available for many parts of the archipelago, and were used wherever available.

In deep water, where high-resolution multibeam data were not available, the

grid was developed by interpolation of a combination of USGS GLORIA

surveys and the Smith and Sandwell 2-min global seafloor dataset.

All selected input datasets were converted to the mean high water (MHW)

vertical datum as necessary. Bathymetric datasets were converted from the

survey tidal datum (usually MLLW or MSL) using offset surfaces interpolated from NOS tide gauges at Kahului, Kawaihae (Hawaii), and Kaunakakai

(Molokai). The CSC IfSAR topographic data as obtained was vertically referenced to the GRS80 ellipsoid. It was converted to MHW using an offset

surface interpolated from seven National Geodetic Survey (NGS) benchmark

stations on Maui that had ellipsoid and tidal heights recorded.

Raw data sources were imported to ESRI ArcGIS-compatible file formats. Horizontal positions were reprojected, where necessary, to the WGS84

horizontal geodetic datum using ArcGIS. In the point datasets, single sounding points that differed substantially from neighboring data were removed.

Gridded datasets were checked for extreme values by examination of contour

lines, and, where available, by comparison between multiple data sources.

To compile the multiple data sources into a single grid, subsets of the

source data were created in the priority order described above. A triangulated irregular network (TIN) was created from the detided vector point data

(geodas, usace, csc lidar). Also added to the TIN were points taken from the

edges of the gridded data regions to ensure a smooth interpolated transition

between areas with different data sources. This TIN was linearly interpolated using ArcGIS 3D Analyst to produce an intermediate 1-arc-sec and

6-arc-sec raster grid. The gridded datasets were then bilinearly resampled

to these resolutions and overlaid on top of the intermediate grids.

4.3 Model Setup

By sub-sampling from the DEMs described in section 4.2, two sets of computational grids were derived, the Kahului Reference Inundation Model (RIM)

(Fig. 11) and the Stand-by Inundation Model (SIM) (Figs. 2.a.1, 2.b.3, and

2.c.3). Each set consists of three levels of telescoped grids with increasing

resolution. The regional grids cover the major Hawaiian Islands and the
Tsunami forecast inundation models for Hawaii 23

Table 3: MOST setup of Kahului RIM and SIM.

Reference Inundation Model Stand-by Inundation Model

(RIM) (SIM)

Coverage Cell Time Coverage Cell Time

Lon. [◦E] Size Step Lon. [◦E] Size Step

Grid Region Lat. [◦N] [] [sec] Lat. [◦N] [] [sec]

A Hawaii 199–205.98 36 1.6 199–205.9667 120 12

18–23 (699 × 500) 18.0317–22.9967 (210 × 150)

B Maui Complex 202.5717–204.098 6 0.4 202.8967–204.0967 12 1.5

20.4–21.3933 (917 × 597) 20.4017–21.255 (361 × 257)

C Kahului 203.4681–203.71 1/3 0.2 203.4869–203.6319 2 1.5

20.8364–20.975 (2613 × 1498) 20.8674–20.9507 (262 × 151)

Minimum offshore depth [m] 20 20

Water depth for dry land [m] 0.1 0.1

Manning coefficient, n 0.01, 0.025, 0.032 0.01, 0.025

CPU time for a 4-hour simulation ∼41 hours <10 minutes

coastal grids cover Maui, Lanai, Kahoolawe, and East Molokai. Run-up and

inundation simulations are calculated in nearshore grids over the study area.

In Fig. 11, the solid boxes in red indicate boundaries of the nested RIM grids

while the dashed boxes in red represent the corresponding boundaries of the

SIM. Grid details at each level and input parameters are summarized in

Table 3.

To reduce numerical instability for certain worst-case scenarios, a large

Manning coefficient may be required. The friction coefficient does not change

the offshore results. Its effect on model inundation will be discussed in

section 4.4.4. For a simulation of a 4-hour event, the optimized SIM takes

less than 10 min of CPU time on a Linux system using a single 3.6 GHz

Xeon processor, while the RIM takes about 41 hours.

4.4 Results and Discussion

4.4.1 Validation and error estimate

Both the reference inundation model and the stand-by inundation model for

Kahului were tested with the 14 historical tsunamis summarized in Table

4. Figure 12 shows the comparisons of observed and modeled time series by

RIM and SIM at Kahului tide station and the corresponding wavelet-derived

amplitude spectra. The description of the time series of wavelet-derived

amplitude spectra can be found in Tang et al. (2008).
24 Tang et al. −4000

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E 201oE 203oE 205oE

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Alenuihaha Ch.

Maui

Molokai

Lanai

Kahoolawe

Kealaikahiki Ch.

Pailolo Ch.

Kalohi Ch.

Auau Ch.

Alalakeiki Ch.

202.8oE 203.4oE 204oE

20.5oN

21.1oN

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E 203.56oE 203.62oE 203.68oE

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20.96oN

(a)

(b)

(c)

Figure 11: Grid setup of the Kahului Reference Inundation Model (RIM). Solid lines represent the telescoping grids. Dashed lines indicate the corresponding boundaries of the Kahului SIM in Fig 2.
Tsunami forecast inundation models for Hawaii 25

Figure 12, 1–3: Observed and modeled time series of (a) wave amplitudes and (b, c, and d) wavelet-derived

amplitude spectra at Kahului tide gage for the 14 historical tsunamis in Table 4. Observations were not

available for the 1946, 1952, and 1960 tsunamis.
26 Tang et al.

Figure 12, 4–6: Observed and modeled time series of (a) wave amplitudes and (b, c, and d) wavelet-derived

amplitude spectra at Kahului tide gage for the 14 historical tsunamis in Table 4. Observations were not

available for the 1946, 1952, and 1960 tsunamis.
Tsunami forecast inundation models for Hawaii 27

Figure 12, 7–9: Observed and modeled time series of (a) wave amplitudes and (b, c, and d) wavelet-derived

amplitude spectra at Kahului tide gage for the 14 historical tsunamis in Table 4. Observations were not

available for the 1946, 1952, and 1960 tsunamis.
28 Tang et al.

Figure 12, 10–12: Observed and modeled time series of (a) wave amplitudes and (b, c, and d) waveletderived amplitude spectra at Kahului tide gage for the 14 historical tsunamis in Table 4. Observations were

not available for the 1946, 1952, and 1960 tsunamis.
Tsunami forecast inundation models for Hawaii 29

Figure 12, 13–14: Observed and modeled time series of (a) wave amplitudes and (b, c, and d) waveletderived amplitude spectra at Kahului tide gage for the 14 historical tsunamis in Table 4. Observations were

not available for the 1946, 1952, and 1960 tsunamis.
30 Tang et al.

The most recent event is the 15 August 2007 Peru tsunami. A detailed

description of the real-time experimental forecast for this tsunami can be

found in Wei et al. (2008). At Kahului tide gage, the observed maximum

wave height is 56 cm while the forecast is 55 cm. A −12-min adjustment was

applied to the modeled time series in Fig. 12.1.a. The modulated amplitude

spectrum in Fig. 12.1.b indicates that two groups of oscillations with peak

periods near 34 and 16 min exist prior to the arrival of the tsunami.

The 13 January 2007 Kuril Islands earthquake occurred as normal faulting. The tsunami moment magnitude 7.9 was inverted from the first waves

recorded at three DARTs, 21414, 46413, and 21413 closest to the epicenter.

This tsunami source overestimates the wave heights at Kahului (Fig. 12.2).

The Kuril Islands tsunami of 15 November 2006 provided ample tsunami

data and the first test of the NOAA new experimental tsunami forecast

system. At Kahului tide station, the largest wave is the 8th wave, which

arrived about 2 hours after the first arrival. That is also the latest arrival

of the maximum wave among the historical tsunamis studied in this report.

The modeled first waves agree well with the observations while the maximum

wave height is underestimated (Fig. 12.3.a).

The 3 May 2006 Tonga earthquake generated a tsunami that was detected about 6 hours later by two offshore DARTs located to the south of

the Hawaiian Islands, the Dart II (station 51407) and a DART ETD that

was under testing. These data were combined with the model propagation

database to produce the tsunami source by inversion (Tang et al., 2008).

Figure 12.4.a compares the observations at Kahului tide station with model

results up to 24 hours after the earthquake. Very good agreement is obtained for the first six waves over 2 hours, including the amplitudes, arrival

time, and wave period. The SIM well reproduced the 4th wave as the maximum, which resulted from the combination of far-field and near-field wave

scattering and was further amplified by the harbor resonance (Tang et al.,

2008). In addition, the Kahului SIM correctly reproduced tsunami waves

reflected from the west coast of North America and those scattered by the

East Pacific Rise that reached the Hawaiian Islands 16 hours and 18.5 hours,

respectively, after the earthquake.

The 17 November Rat Islands tsunami provided the first genuine test

of PMEL’s forecast methodology (Titov et al., 2005). This tsunami was

detected by three DARTs located along the Aleutian Trench. The real-time

data was combined with the propagation database to produce the earthquake

source by inversion. Titov et al. (2005) showed excellent agreement between

the model prediction and observed data at Hilo tide gage. The same source

was applied here and the results are plotted in Fig. 12.5. Both RIM and

SIM correctly produced amplitudes, arrival time, and periods for the first

several waves. The wave amplitude decreased quickly and steadily.

The 25 September 2003 Hokkaido earthquake generated tsunami waves

of very long periods. Kahului tide station recorded first waves with peak

periods near 34 min. The wave amplitude decreased slowly and steadily

(Fig. 12.6).

DART buoy 51406, located midway between South America and Hawaii

at 8◦29

19S 125◦020W, was not deployed until 1 month after the 23 June
Tsunami forecast inundation models for Hawaii 31 Table 4: Tsunami sources and maximum wave height recorded at Kahului tide station for 14 historical tsunamis. Seismic Tsunami Earthquake Location moment moment Obs. Tsunami Date Time Lat Lon Sub. magnitude magnitude Hmax No. ID Area (UTC) (◦) (◦) zone (Mw) (TMw) (m) Tsunami source 1 200708 Peru 2007.08.15 23:40:57 13.354S 76.509W SASZ 8.0 (CMT) 8.1 0.57 14.1*a9+4.32*b9 2 200701 Central Kuril Is. 2007.01.13 04:23:20 46.272N 154.455W KKJI 8.1 (CMT) 7.9 0.33 –3.64*b13 3 200611 Central Kuril Is. 2006.11.15 11:14:17 46.607N 153.230E KKJI 8.3 (CMT) 8.1 1.47 14*a12+0.5*b12+2*a13+1.5*b13 4 200605 Tonga 2006.05.03 15:26:39 20.13N 174.164W NZKT 8.0 (CMT) 8.0 0.49 6.6*b29 5 200311 Rat Is. 2003.11.17 06:43:07 51.13N 178.74E AACC 7.7 (CMT) 7.8 0.66 12.81*b11 6 200309 Hokkaido 2003.09.25 19:50:06 42.4N 143.15E KKJI 8.3 (CMT) 8.0 0.36 3.6m*(100 × 100 km), 109#rake, 20#dip, 230#strike, 25m depth 7 200106 Peru 2001.06.23 20:33:14 16.14S 73.31W SASZ 8.4 (CMT) 8.2 0.67 5.70*a15+2.90*b16+1.98*a16 8 199606 Andreanof 1996.06.10 04:04 51.478N 176.847E AACC 7.9 (CMT) 7.8 0.57 2.40*a15+0.80*b16 9 199410 East Kuril Is. 1994.10.04 13:22:58.3 43.706N 147.328E KKJI 8.3 (CMT) 8.1 0.69 9.00*a20 10 196403 Alaska 1964.03.28 03:36:14 61.04N 147.73W AACC 9.2 (USGS) 29.0 3>3.46 Tang et al. (2006) 11 196005 Chile 1960.05.22 19:11:14 45.88S 76.29W SASZ 9.5 (Kanamori n/a and Cipar, 1974) 12 195703 Andreanof 1957.03.09 14:22:31 51.63N 175.41W AACC 8.6 (USGS) 28.7 3>3.50 31.4*a15+10.6*a16+12.2*a17 13 195211 Kamchatka 1952.11.04 16:58:26.0 52.75N 159.50E KKJI 9.0 (USGS) 28.7 n/a 14 194604 Unimak 1946.04.01 12:28 52.75N 163.5E AACC 8.5 (Lopez 28.5 n/a 7.5*b23+19.7*b24+3.7*b25 and Okal, 2006) 1: Forecast tsunami source. 2: Preliminary result. 3: Trough reached gage limit.
32 Tang et al.

2001 Peru tsunami. Therefore, the source for this event was derived based

on an inversion of Kahului tide station records using the Kahului SIM. Six

tsunami source functions, AB 15 to 17 along the South American subduction

zone near the epicenter, were involved. The linear least squares inversion

estimates a magnitude of 8.2. In addition to Kahului, it produced good

comparisons of first waves at Honolulu and Hilo tide stations. Figure 12.7.a

shows that the wave amplitude keeps the same magnitude as the first waves

even 14 hours after the first arrival. The underestimation of the model wave

heights for the later waves near t = 20 hours is also due to the lack of

long-period components (Figs. 12.7.a, 12.7.b, and 12.7.c).

Deep-ocean BPR data are also available for two other tsunamis. The inversion of the 10 October 1994 Kuril Islands data was done by using five BPR

recordings, while the 10 June 1996 Andreanov used only one. Model results

agree quite well with Kahului tide station records for the first several waves

(Figs. 12.8 and 12.9), especially the 1994 Kuril Islands tsunami. Though

the models missed the second wave, they described the third through sixth

large waves along the wave chain well (Fig. 12.9.a).

The limited number of DART buoy records does not include any of the

destructive tsunamis described in section 2.1. Previous studies of seismic,

geodetic, and water-level data have estimated source parameters for some

of the events (Kanamori and Ciper, 1974; Johnson et al., 1994; 1996; Johnson and Satake, 1999). However, those sources are subject to debate and

adjustment. Most of the source estimates that have been done are based

on low-resolution tsunami propagation models. The SIMs that have been

developed at NCTR provide a unique chance to re-investigate the historical

sources by inversion of the water level data with the high-resolution quality

inundation and propagation models. Preliminary results are available for

the 1964, 1957, 1952, and 1946 tsunamis. The fault parameters of the 22

May 1960 Chile tsunami are taken from Kanamori and Ciper (1974). Model

results are plotted in Figs. 12.10, 12.11, 12.12, 12.13, and 12.14. The wave

amplitude of the 1960 Chile tsunami decayed slowly.

Error estimates of the maximum wave height and arrival of the first

wave peak computed by the Kahului SIM for eleven historical tsunamis

are presented in Figs. 13.a and 13.b. When the observed maximum wave

height is between 0.3 to 0.5 m, the error is within ±50%. The low signalto-noise ratio of the observations and the low ratio of signal to uncertainty

from the model setup are the major contributions to the error. When the

maximum wave height is greater than 0.5 m, the error reduces to within

±20%, which can be attributed mainly to uncertainties from the tsunami

source, model setup, and bathymetry. First arrivals in general agree well

with the observations, with errors less than ±3% of the travel time. So

far, the largest discrepancy between the modeled and observed first arrival

time is −12 min for the 200708 Peru tsunami. However, with an earthquake

epicenter 460 km to the northwest of the 200708 Peru earthquake, the arrival

of the 200106 Peru tsunami has only a −3-min discrepancy. This −12-min

arrival discrepancy is currently under investigation.

To further explore the tsunami frequency responses at Kahului, Fig. 13c

compares the eleven observed and modeled peak wave periods from the am-
Tsunami forecast inundation models for Hawaii 33

0 0.5 1 1.5 2 2.5 3 3.5 4

−50

−40

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0

10

20

30

40

50

200708

200701

200611

200605

200311

200309

200106

199606

199410

196403

195703

Maximum wave height, Hobs (m)

Error, (

Hsim−Hobs)/

Hobs *100%

(a)

SASZ

KKJI

NZKT

AACC

2 4 6 8 10 12 14 16

−4

−3

−2

−1

0

1

2

3

4

200708

200701

200611

200605

200311

200309

200106

199606

199410

196403

195703

Arrival of the first peak, t

obs (hour)

Error, (tsim−tobs)/tobs *100%

(b)

8 12 16 20 24 28 32 36 40

8

12

16

20

24

28

32

36

40

200708

200701

200611 200605

200311

200309

200106

199606

199410

196403 195703

Peak wave period, Tobs (min)

Tsim , (min)

group 1 group 2 group 3

(c)

Figure 13: Comparison and error estimation of (a) maximum wave height, (b) arrival of the first wave

peak, and (c) peak wave period of observations and model results from the Kahului SIM.
34 Tang et al.

plitude spectra in Fig. 12. The observed peak wave periods fall into one of

the three groups of 16-, 24-, or 34-min periods (±2 min). This indicates that

the peak wave period is usually one of the local resonant frequencies. An interesting question is, for a particular tsunami, which local frequency will be

the peak frequency? Figure 13c indicates that it is mainly related to the geographic location of the earthquakes. Tsunamis originating from the nearby

subduction zone earthquakes generate similar peak frequencies at Kahului.

For example, the 200611 and 200701 Central Kuril Islands tsunamis have

a peak period near 16 min (group 1), while the 199410 West Kuril Islands

tsunami and the nearby 2003 Hokkaido tsunami present the same peak period near 34 min (group 3). The remaining seven tsunamis have similar

peak wave periods near 24 min (group 2). The Kahului SIM correctly reproduced the peak wave periods within groups 2 and 3. However, there are

discrepancies between the modeled and observed peak periods in group 1 for

the 200611 and 200701 Kuril Islands tsunamis. Though the 16-min period

(group 1) appears in the modeled amplitude spectra, the Kahului SIM for

those tsunamis shows a peak period near 24 min (Fig. 12.2 and 12.3). The

deep-ocean tsunami observations at DARTs for these two events show that

high-frequency components appear in the later wave chains, which were not

well resolved in the propagation models. This may cause the peak period

computed by the Kahului SIM to be shifted from group 1 to group 2.

To explore the hazard wave conditions over the entire study area, computed maximum water elevation above MHW and maximum velocity of the

fourteen tsunamis are plotted in Fig. 14. Both the RIM and SIM produced

similar patterns and values. In general, the maximum water elevation exhibits two typical patterns, (1) gradually increasing elevation toward Kahului

Harbor, such as the 2003 Hokkaido tsunami (Fig. 14.6); and (2) dramatically

increasing elevation near the coastline, such as the 1946 Unimak tsunami

(Fig. 4.14). These patterns relate to the tsunami wave periods.

4.4.2 Assessment of potential impact for Kahului from simulated TMw

7.5, 8.2, 8.7, and 9.3 tsunamis

Located in the middle of the Pacific, Kahului is potentially vulnerable to a

variety of Pacific-wide tsunamis. At what magnitude from which location on

a subduction zone can a tsunami have a devastating impact on the community? Assessment of the potential impact can provide useful and important

information in advance of a real event. The validated Kahului SIM, which

was optimized for speed and accuracy, along with the forecast propagation

database, provide powerful tools to address this problem.

Even construction of tsunamis of the same magnitude can be enormous

with various numbers of tsunami source functions and coefficients. For simplicity, here we apply a uniform coefficient to tsunamis of the same magnitude. Four different magnitudes, TMw 7.5, 8.2, 8.7, and 9.3 were tested.

The details of the simulated tsunami sources and results are summarized

in Table 5 and Fig. 15. The maximum water elevation, ηmax, at Kahului

tide station from TMw 7.5 tsunamis computed by the SIM is plotted in bars

in Fig. 15b. Color represents the first arrival at the station, which is the
Tsunami forecast inundation models for Hawaii 35

Table 5: Simulated tsunamis for hazard assessment study for Kahului.

Numbers Tsunami Numbers Range of ηmax Ratio

TMw of TSFs source coef. Lines of tests min max max/min

1 7.5 1 1 BA 804 0.005 cm 1.90 cm 380

2 7.5 1 1 BA 804 0.05 cm 28.5 cm 570

3 8.2 1 10 B 405 0.01 m 1.55 m 155

4 8.7 6 (3 pairs) 12 BA 381 0.06 m 2.88 m 48

5 9.3 20 (10 pairs) 29 BA 294 0.56 m 9.26 m 17

1: at Kahului offshore from the pre-computed propagation database; 2 to 5: at Kahului station computed

by the Kahului SIM.

time of the water level reaching a height of 20% of the first significant peak

or trough. Bars in Fig. 15a indicate the maximum elevation at deep water

offshore Kahului from the same sources, which are from the propagation

database. Figures 15c, d, and e show ηmax at Kahului tide station from TMw

8.2, 8.7, and 9.3 tsunamis, respectively. The color represents the difference

in time between the arrival of the maximum elevation, tmax, and first arrival,

t1.

Tsunami waves in the study area generated by the same magnitude

tsunamis from the major subduction zones in the Pacific can vary significantly. Test results in Table 5 show that the ratio of maximum to minimum

ηmax at the station from the same magnitude tsunamis varies from 570 to 17,

with TMw ranging from 7.5 to 9.3. This indicates that moment magnitude

alone is inadequate to provide warning guidance for coastal communities,

since it contains information related only to the source. This is only the

first stage of the three distinct stages of earthquake-generated tsunami, generation, deep-ocean propagation, and coastal transformation. An accurate

forecasting and warning system must also take into account the next two

stages. SIMs contain local bathymetric and topographic information and

utilize the dynamic boundary conditions from the propagation database.

They are designed to provide accurate forecasting for site-specific coastal

communities and to avoid false alarms resulting from incomplete information. By combining DART inverted tsunami magnitude together with sitespecific SIMs, the forecast can completely cover the three distinct stages of

the earthquake-generated tsunamis.

Tsunami sources on the Kamchatka and the Aleutian-Alaska-CanadaCascadia (AACC) subduction zones can generate relatively large waves in

Kahului (Fig. 15). One reason could be that Kahului is unprotected from

these directions. Late arrival of the maximum wave can be expected from

subduction zones in the southwest and west Pacific. Historically, earthquakes

at the Kamchatka, Aleutian Alaska, and South America Subduction Zones

produced significantly larger tsunami waves. The 1952 Kamchatka, 1946

Unimak, and 1960 Chile earthquakes occurred in these subduction zones,

and each had devastating impacts in Kahului. As described by Titov et al.

(1999), the amplitude of the offshore propagating tsunami could vary significantly by its source location, cylindrical spreading, and directionality of

the tsunami wave pattern. Cylindrical spreading decreases tsunami offshore
36 Tang et al.

Figure 14, 1–7: Maximum water elevation and maximum velocity computed by the Kahului RIM and SIM

for the 14 historical tsunamis.
Tsunami forecast inundation models for Hawaii 37

Figure 14, 8–14: Maximum water elevation and maximum velocity computed by the Kahului RIM and

SIM for the 14 historical tsunamis.
38 Tang et al.

260 280

0

0.25

0.5

0.75

1

(cm) 

ηmax

220 240

Kahului offshore

140 160 180 200

−40

−20

0

20

40

60

(a) TMw = 7.5

260 280

0

2.5

5

7.5

10

(cm) 

ηmax

220 240

Kahului tide station 

140 160 180 200

−40

−20

0

20

40

60

(b) TMw = 7.5

 (hour) 

16.3

14.8

13.3

11.8

10.3

8.8

7.3

5.8

4.2

t

1

260 280

0

0.25

0.5

0.75

1

(m) 

ηmax

220 240

Kahului tide station 

140 160 180 200

−40

−20

0

20

40

60

(c) TMw = 8.2

 (hour) 

4.0

3.5

3.0

2.5

2.0

1.5

1.0

0.5

0.0

t

max

− t

1

260 280

0

0.25

0.5

0.75

1

(m) 

ηmax

220 240

Kahului tide station 

140 160 180 200

−40

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0

20

40

60

(d) TMw = 8.7

 (hour) 

4.0

3.5

3.0

2.5

2.0

1.5

1.0

0.5

0.0

t

max

− t

1

9

10

280

8

260

0

1

2

3

4

(m) 

ηmax 7

240

6

5

220

Kahului tide station 

4

200

3

11

12

180

13

2

160

14

1

18

140

15

17

16

−40

−20

0

20

40

60

(e) TMw = 9.3

 (hour) 

4.0

3.5

3.0

2.5

2.0

1.5

1.0

0.5

0.0

t

max

− t

1

Figure 15: Maximum water elevation at (a) Kahului offshore from the propagation database and (b, c,

d, and e) at Kahului tide station computed by the Kahului SIM for simulated TMw 7.5, 8.2, 8.7, and 9.3

tsunamis. Colors in (b) represent the first arrival at the station. Colors in (c), (d), and (e) represent the

difference in time between the arrival of the maximum elevation and the first arrival.
Tsunami forecast inundation models for Hawaii 39

wave amplitude with increasing distance from the source. On the other hand,

the shape of a tsunami source and bathymetric profile near the subduction

zone makes tsunami energy very directional, with most of the wave energy

propagating at a right angle to the earthquake fault. When the path from

the tsunami source to Kahului coincides with the propagation direction of

the main wave energy and the incident tsunami frequencies are within the

right ranges, large tsunami waves can be generated nearshore.

4.4.3 Robustness and stability

Recorded historical tsunamis provide only a limited number of events, from

limited locations. More comprehensive test cases of destructive tsunamis

with different directionalities are needed to check the stability and robustness

of SIMs. A set of 18 simulated TMw 9.3 tsunamis (Fig. 15e) was selected here

for further examination. The SIM results are compared with those from the

high-resolution RIM in Figs. 16 and 17. Waveforms computed by the SIM

agree well with those from the RIM (Fig. 16). The SIM and RIM compute

similar maximum water elevation and inundation in the study area (Fig. 17).

These results indicate that the Kahului SIM is capable of providing robust

and stable predictions of long duration for Pacific-wide tsunamis.

Tsunami waves in the study area vary significantly for the 18 TMw 9.3 scenarios. The maximum water elevation at the gage ranges from 1.4 m to 9.3 m

for the Tonga (No. 11) and Kamchatka (No. 2) scenarios. These results show

the complexity and high nonlinearity of tsunami waves nearshore, which

again demonstrate the value of SIMs for providing accurate site-specific forecast details.

4.4.4 Inundation tests

Sensitivity of inundation to the grid resolution for the study area was discussed in section 3.2. In this section, we focus on the sensitivity of inundation

computed by the Kahului SIM to the friction coefficient.

Runup data are available for Kahului for the 1946, 1957, 1960, and

1964 tsunamis (Pararas-Carayannis, 1969; Walker, 2004). The 1946 Alaskan

tsunami has the most run-up data, with nine points in the study area. Therefore it is selected as the test case. The run-up survey points, after conversion

from an assumed original Old Hawaiian Datum to the WGS84 horizontal

datum that the topography and shorelines are referenced to, are plotted

as black cross symbols in Fig. 18a. The quality of the measurements is

ambiguous, since some points fall within the ocean. Figure 18a shows inundation in the Kahului nearshore grid computed from three different Manning

coefficients, n = 0.01, 0.025, and 0.032. The coefficients generate similar inundation lines for most of the coastline where the slope is relatively steep.

However, a small Manning coefficient of 0.01 produces further inundation at

several flat areas, such as the southeast area adjacent to Kahului Harbor,

including the Maui Mall, the Kanaha Ponds, and the Lower Paia. The waterfront to the southeast of Kahului Harbor has a flat slope of 0.0019 from

2-m topographic contour down to the shoreline. Figure 18b shows the in-
40 Tang et al.

3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 −2

0

2

4

6

(1) KKJI AB22T31 RIM

SIM

3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 −2

0

2

4

6

8

10

(2) KKJI AB1T10

3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 −2

0

2

4

6

8

10

(3) AACC AB16T25

3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 −2

0

2

4

6

η (m)

(4) AACC AB22T31

3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 −2

0

2

4

6

8

10

(5) AACC AB50T59

3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 −2

0

2

4

6

(6) AACC AB56T65

3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 −2

0

2

4

6

(7) CASZ AB1T10

3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 −2

0

2

4

6

(8) CESZ AB1T10

3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 −2

0

2

4

6

t (hour)

(9) SASZ AB40T49

3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 −2

0

2

4

6

(10) SCSZ AB3T12

3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 −2

0

2

4

6

(11) NZKT AB20T29

3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 −2

0

2

4

6

(12) NZKT AB30T39

3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 −2

0

2

4

6

(13) NBSV AB28T37

3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 −2

0

2

4

6

(14) MOCB AB1T10

3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 −2

0

2

4

6

(15) NNGZ AB3T12

3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 −2

0

2

4

6

(16) EPSZ AB6T15

3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 −2

0

2

4

6

(17) RKNZ AB12T21

3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 −2

0

2

4

6

t (hour)

(18) KKJI AB32T41

Figure 16: Tsunami time series at the Kahului tide station computed by the RIM and SIM from a set of

simulated TMw 9.3 earthquakes. The label, for example, “KKJI AB22T31” in (1), indicates that the tsunami

source is comprised of sources No. 22 to 31 on both A and B lines along the KKJI subduction zone.
Tsunami forecast inundation models for Hawaii 41

Figure 17: Maximum water elevation in the study area generated by the same set of 18 simulated TMw 9.3

tsunamis as in Fig. 16.
42 Tang et al.

undation computed with n = 0.025 and 0.032 for the TMw 9.3 Kamchatka

scenario (No. 2). Though there are some minor differences at several local

areas, the inundation limit agrees well for this test case.

In general, a smaller Manning coefficient can produce further inundation

at some flat areas for certain test cases. However, the model can become

unstable with a small Manning coefficient for large tsunami waves, such as

n = 0.01 for the TMw 9.3 Kamchatka scenario, from which the maximum

elevation exceeds 9 m at Kahului tide station. Therefore, for the forecast

operational purpose, we suggest n = 0.01 to n = 0.025. Meanwhile, we

suggest considering the waterfront area to the southeast of Kahului Harbor,

including the Maui Mall, the Kanaha Ponds, and the Lower Paia, as areas of

inundation uncertainty due to lack of measurements to calibrate the Manning

coefficient. The computed time series of tsunami elevation at Kahului gage

is insensitive to changes in the Manning coefficients.

5. Summary and Conclusions

Sensitivity studies of tsunami wave nearshore characteristics and inundations

were conducted for ranges of model grid setups, resolutions, and parameters.

Based on these studies, procedures and testing of validation, robustness, and

stability were suggested for developing tsunami forecast inundation models

(Stand-by Inundation Models, or SIMs).

A SIM was developed for the coastal community of Kahului, Hawaii. The

computational grids for the Kahului SIM were derived from the best available

bathymetric and topographic data sources. The model was tested with 14

historical tsunamis and different scenarios of simulated TMw 7.5, 8.2, 8.7,

and 9.3 tsunamis based on subduction zone earthquakes in the Pacific. The

SIM outputs are compared to both historical water level data and numerical

results from a reference inundation model (RIM) of higher resolution.

The accuracy of the maximum wave height computed by the Kahului SIM

is greater than 80% when the observed maximum wave height is greater than

0.5 m, and 50% when the observation is between 0.3 to 0.5 m. The error of

the modeled first arrivals is within ±3% of the travel time. Wavelet analysis

of the observed time series tsunami amplitude at Kahului indicates that the

peak wave period mainly falls into one of the three local 16-, 24-, or 34-min

resonant periods (±2 min). Which resonance period will be the peak period

at Kahului is relevant to the geographic location of the tsunami sources.

The optimized SIM can accurately provide a 4-hour site-specified forecast

of first wave arrival, amplitudes, and reasonable inundation limit within

minutes of receiving tsunami source information constrained by deep-ocean

DART measurements. It is also capable of reproducing later tsunami waves

reflected or scattered by far-field bathymetry that may arrive hours after the

first arrival.

A tsunami could strike Kahului with large waves from the Kamchatka,

Alaska-Aleutian, Canada, Cascadia, and South America subduction zones.

The Aleutian tsunami has the shortest first arrival at the Kahului gage of
Tsunami forecast inundation models for Hawaii 43

203.5 203.52 203.54 203.56 203.58 203.6 203.62

20.86

20.87

20.88

20.89

20.9

20.91

20.92

20.93

20.94

20.95

2

2

2 2

2

2

2

2

2 2

2

2

2

2

2

2

2

2

2

2

2

2

2

2 2

2

5

5

5

5

5

5

5

5

5

5

5 5

5

5

5

5

5

5

10

10

10

10

10

10

10

10

10

10

10

10

10

10 10

10

20 20

20

20

20

20

20

20

20

20

20

20

20

20

20

20

20

(a) 1946 Unimak tsunami

n = 0.01

n = 0.025

n = 0.032

3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5

−2

−1

0

1

2

time, (hour)

elev., (m)

Kahului tide gage

203.5 203.52 203.54 203.56 203.58 203.6 203.62

20.86

20.87

20.88

20.89

20.9

20.91

20.92

20.93

20.94

20.95

2

2

2

2

2 2 2 2

2 2

2

2

2

2 2

2

2 2

2

2

2

2

2

2

5

5

5

5

5

5

5

5

5

5

5

5

5

5

5

5

5

5

10

10

10

10

10

10

10

10

10

10

10 10

10

10

10

20

20

20

20

20

20

20

20

20

20

20

20

20

20

20

20

20

 (b) Simulated Kamchatka Tsunami (No. 2 Scenario) 

n = 0.025

n = 0.032

5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10

0

5

10

time, (hour)

elev., (m)

Kahului tide gage

Figure 18: Sensitivity of inundation and time series of tsunami amplitudes computed by the Kahului SIM

to Manning coefficients for (a) the 1946 Unimak tsunami, and (b) the simulated TMw 9.3 Kamchatka tsunami

(No. 2).
44 Tang et al.

4.25 hours. Special attention must also be paid to the locations from which

the main offshore wave energy propagates toward the Hawaiian Islands, including the East Philippines and Marianas Subduction Zones to the east,

and Vanuatu to the southeast. In addition to Kahului Harbor, larger waves

may be expected at Waiehu Pt. and Sprecklesville from tsunamis when the

peak period is near 16 min or less. The study suggests considering the waterfront area to the southeast of Kahului Harbor, including the Maui Mall,

the Kanaha Ponds, and the Lower Paia, as areas of inundation uncertainty

due to the lack of measurements to calibrate the friction coefficient for the

SIM.

The tsunami hazard assessment study for Kahului shows tsunami waves

nearshore can vary significantly from the same magnitude tsunamis from different subduction zones or from different locations on the same subduction

zone. As a consequence, the moment magnitude alone is inadequate to provide warning guidance for coastal communities, since it contains information

related only to the source. This is only the first stage of the three distinct

stages of earthquake-generated tsunami, generation, deep-ocean propagation, and coastal transformation. By including local bathymetry and topography and utilizing the dynamic boundary conditions from the propagation

database, SIMs are designed to provide accurate site-specific forecasting for

coastal communities, thus avoiding false alarms resulting from incomplete

information. Only by combining the DART-constrained tsunami magnitude

together with site-specific SIMs can the forecast completely cover the three

distinct stages.

6. Acknowledgments

Special thanks to Dr. Elena Tolkova’s extensive assistance in pre-processing

model input, MOST versioning, and post-processing data. We thank Dr.

Mick Spillane for providing information on Kahului offshore; Dr. Harold

Mofjeld, Marie Eble, Nazila Merati, Clyde Kakazu, and Allison Allen for

assistance with tide gage data; Drs. Robert Weiss, Diego Arcas, and Yong

Wei for discussion; Dr. Edison Gica and Jean Newman for assistance with

the propagation database. The authors are grateful to Ryan Layne Whitney

for his valuable comments, editing, and corrections.

This research is funded by the NOAA Center for Tsunami Research

(NCTR), PMEL Contribution #2985. This publication is partially funded

by the Joint Institude for the Study of the Atmosphere and Ocean (JISAO)

under NOAA Cooperative Agreement No. NA17RJ1232, PMEL Contribution #1310.
Tsunami forecast inundation models for Hawaii 45

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