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Figure 3. High-resolution tsunami inundation forecasts at the Makauwahi Sinkhole
on Kaua‗i are shown, respectively, for the Mw 9.25 events in Figure 1. The map scale
is about 321 m on a side. Only the east Aleutian earthquake (upper left) inundates the
sinkhole, reaching 8 to 9 m above mean sea level. The center of the sinkhole is
indicated with a small magenta dot.
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Online supplementary material for
Paleotsunami Evidence on Kaua‘i and Numerical Modeling
of a Great Aleutian Tsunami
Rhett Butler1, David Burney2, and David Walsh3
[1] These supplementary materials provide additional information regarding (1)
legendary tsunamis in Hawai‘i; (2) the setting of the Kaua‘i paleotsunami deposit, (3)
detailed methods and models used in the tsunami forecasts; (4) tsunami sensitivity to the
sinkhole topography; and (5) alternate hypotheses for the Kaua‘i tsunami deposit. Two
tables of earthquake source characteristics are included with additional figures illustrating
the main text.
1. Legendary Hawaiian References to Tsunamis
[2] The date is 1500-1600. The earliest reference to a tsunami in Hawaii came from
the following chant attributed to Huluamana and composed in the 16th century: “The sun
shines brightly at Kalaeloa which sank into the sea. A huge wave came and killed its
inhabitants scattering them and leaving only Papala‘au; their cries are all about.” It
describes a tsunami like event on the west coast of Moloka‘i [Lander and Lockridge,
1989].
[3] There is a historical reference in native Hawaiian lore regarding a prior large
tsunami just north of Kaneohe. “The land now called Kualoa was formerly Paliku
[upright cliff], for its salient feature, the great cliff at its back. It was here that the
primordial goddess Haumea battled alone against the warriors of Kumuhonua in
1 Hawai‘i Institute of Geophysics and Planetology, University of Hawai‘i at Manoa, Honolulu, HI 2 National Tropical Botanical Garden, Kalaheo, HI 3 Pacific Tsunami Warning Center, Honolulu, HI
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legendary times preceding the great tidal wave that inundated all the coast from Kualoa
south to He‘eia. Here was built the high shrine to Lono, the god of storm, who saved
Wakea and Haumea in the flood.” [Handy and Handy, 1972; Carson and Athens, 2007]
2. Setting of the Makauwahi Sinkhole on Kaua‘i
[4] The setting for the paleotsunami study in maps, diagrams, and photos of the site
and the deposit is presented in Figures S1, S2, and S3.
3. Methods and Models
3.1 Computational Method
[5] We use NEOWAVE (Non-hydrostatic Evolution of Ocean Wave) of Yamazaki et
al. [2009, 2011b] to model each tsunami from generation at the earthquake source to
inundation at the coastline of Kaua‘i. The staggered finite difference model builds on the
nonlinear shallow-water equations with a momentum conservation scheme to
approximate breaking waves as bores or hydraulic jumps as in a finite volume model
[e.g., Wei et al., 2006; and Wu and Cheung, 2008]. The code accommodates up to five
levels of two-way nested grids to describe processes of different time and spatial scales
from the open ocean to the coast.
[6] NEOWAVE has been validated against the benchmarks put forth by the National
Tsunami Hazard Mitigation Program and the National Science Foundation, and is
approved by the National Ocean and Atmospheric Agency (NOAA) for use in tsunami
inundation mapping [Yamazaki et al., 2012a]. NEOWAVE has been validated with near
and far-field measurements from the 2009 Samoa, 2010 Mentawai, 2010 Chile, 2011
Tohoku, 2012 Haida Gwaii, and the 2013 Santa Cruz Islands tsunamis [Lay et al., 2011a,
2011b, 2013a, 2013b; Roeber et al., 2010; Yamazaki and Cheung, 2011; Yamazaki et al.,
2011a, 2011c, 2012b, 2013].
[7] For calculation of tsunami forecasts for the Japanese and Pacific West Coasts, we
used the SIFT (Short-term Inundation Forecast for Tsunamis) computer code [Titov and
González, 1997; Titov and Synolakis, 1998; Titov et al., 2005; Gica et al., 2008; Tang et
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al., 2009; references contain extensive method validations] of the National Oceanic and
Atmospheric Administration (NOAA). Complete inundation forecasts were computed
using the NOAA Stand-by Inundation Models (SIMs) for 20 harbors along the Pacific
Coast. SIMs were not available for Japanese harbors, and tsunami amplitudes at the
100 m bathymetry contour were extrapolated to the coast.
3.2 Digital Elevation Model
[8] The National Geophysical Data Center (NGDC) ETOPO1 Global Relief Model at
1 arcmin resolution [Amante and Eakins, 2009] is used for modeling Pacific basin-wide
tsunami propagation. ETOPO1 has approximately 1850 m resolution near the Hawaiian
Islands, where higher-resolution datasets are used. The majority of the offshore
bathymetry is the 1.5 arcsec (46-m) resolution University of Hawai'i SOEST multibeam
data and the gaps are filled by the 5 arcsec (154-m) U.S. Geological Survey (USGS) I-
2809 dataset. The near-shore bathymetry source is the SHOALS (Scanning Hydrographic
Operational Airborne LiDAR Survey) dataset, which was procured by the US Army
Corps of Engineers (USACE) between 1999 and 2004. The data extends from the
shoreline to approximately 40 m water depth at 4-m horizontal resolution. Data from
hydrographic surveys and nautical charts supplements the near-shore bathymetry, mostly
inside harbors and marinas.
[9] The topography is from the USGS 0.33 and 1 arcsec (10 and 30-m) Digital
Elevation Models, which include the SRTM (Shuttle Radar Topography Mission) data.
LiDAR (Light Detection and Ranging) topography data are used near the Kaua‘i coastline
with 1-m horizontal resolution extending from the shoreline to the 15 m elevation
contour—the data for the north and south facing shores procured by USACE and Federal
Emergency Management Agency, respectively. NB: the small portal opening to the
sinkhole within the north cave is not considered in the model. The Generic Mapping
Tools (GMT) of Wessel and Smith [1991] is utilized to merge these DEM data sources,
and extract the computational grids for tsunami modeling.
[10] This study implemented four levels of nested grids to model tsunami propagation
across Pacific and inundation at Kaua‘i coastal area a vicinity of the Makauwahi
sinkhole. The level-1 grid at 2 arcmin resolution (~3000 m) extends the North Pacific
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Ocean to describe tsunami generation and propagation. The level-2 grid at 15 arcsec
(~463 m) and the level-3 grids at 3 arcsec (~90 m) resolve tsunami transformation around
Hawaiian Islands and the Kaua‘i Island, respectively. The level-4 grid at 0.3 arcsec (~9
m) is located southeast of Kaua‘i to model near shore wave transformation and
inundation around Makauwahi sinkhole. It will be noted that ~9 m is approaching the
limit of resolving the features of the sinkhole.
[11] For the SIFT/SIM tsunami forecasts along the Pacific West Coast, the initial
forecasts were pre-computed at 4-arcminute resolution in the open ocean, and stored at
16-arcmin resolution. Nested grids are used in the SIMs to achieve successively greater
detail [Tang et al., 2009]: a regional grid of 2-arcmin (∼3700 m), intermediate grids of
12-18 arcsec (∼370–555 m) at the Makauwehi coast and elsewhere, and a harbor region
grid of about 2-arcsec (∼60 m) resolution.
3.3 Earthquake Sources
[12] Nine earthquake sources with moment-magnitude 9.25 ≥ Mw ≤ 9.6 were
distributed along the Aleutian-Alaska and Kamchatka subduction zones to assess the
tsunamigenic effects in Hawai‘i using the extreme faulting parameters observed globally
in the largest megathrust earthquakes of the last 100 years (see Supplementary Material
Tables S1 & S2). The Mw 9.5 Chilean earthquake had about 35 m of fault slip averaged
over the fault surface, derived from the largest seismic studies [Kanamori and Cipar,
1974; Cifuentes, 1989; Butler, 2012]. Even for the smallest overall estimates for this
earthquake, about 35 m of slip was observed in a segment of the earthquake equivalent to
a Mw 9.0 event itself [Moreno et al., 2009]. The 2004 Mw 9.3 Sumatra-Andaman
earthquake demonstrated extreme length of faulting, extending about 1400 km long
[Ammon et al., 2005; Stein and Okal, 2007; Tsai et al., 2005]. The 2011 Mw 9.1 Tohoku,
Japan earthquake, though relatively short in length (<450 km), showed extreme slip of
greater than 50 m at the shallowest portion of the fault near the subduction zone trench,
which further enhanced the tsunami [Lay et al., 2011b; Yamazaki et al., 2011c].
[13] Each of the scenarios that included the eastern Aleutian segment (Figure S4) of
the subduction zone focused tsunami energy toward the Hawaiian Islands (Figure S5).
Faulting scenarios also considered ruptures extending ≥ 1,000 km both eastward and
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westward from the eastern Aleutian section (Figure S4), to model effects resultant from
an event similar to the 2004 Sumatra-Andaman earthquake. Summarizing, tsunami
effects in Hawai‘i are compared and contrasted in Figure 3, for earthquakes of
comparable size and dimension located adjacent to the Eastern Aleutians and also in
Kamchatka.
4. Tsunami Sensitivity to Sinkhole Topography
[14] Tsunami forecasts for each of the earthquakes that ruptured across the eastern
Aleutians in Table S1 inundate the sinkhole to a sufficient depth to have overtopped a
7.2 m wall. Using the same 35 m fault slip, great earthquakes outside of this tectonic
region could not do so. Since the smallest earthquake capable of inundating the sinkhole
was a Mw 9.25 event within the eastern Aleutians, the effect of decreasing the uniform
slip from 35 to 17.5 m are reviewed in Figure S7.
[15] Care must be taken in interpreting Figures 3 and S7. Since the pixel resolution is
~9 m, features smaller that this are naturally averaged over. The eastern wall of the
sinkhole is less than 9 m in thickness, and hence when averaged across the sinkhole and
exterior slope, the height is effectively decreased to about ~4 m. In the panel of
inundation maps shown in Figure S7 for eastern Aleutian events in Table S2, only the 35
m uniform fault slip reaches the >7 m height of the actual sinkhole, and overtops it with
margin. For uniform fault slip a value of 30 m results in amplitudes ~6.5 m, with
concomitant decrease for smaller values of slip.
5. Alternate Hypotheses
[16] Although the link between the eastern Aleutians and the Kaua‘i paleotsunami
deposit is compelling, we also reviewed other possible sources. For other distant, giant
earthquake sources, the inundation necessary to form the Kaua‘i deposit could not be
achieved, even assuming fault parameters corresponding to the largest historic
observations. Local Hawaiian sources were considered. The Big Island has experienced
earthquakes generating tsunamis. The most recent and best studied is the 1975 Kalapana
earthquake (Mw 7.7) on the south flank of Kilauea [e.g., Ma et al., 1999]. This event
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produced a tsunami at the tide gauge in Nawiliwili harbor of 0.1 m (NGDC). Even a
Mw 8 event, which is three times more energetic, along the southern coast of the Big
Island would not produce a large tsunami on Kaua‘i. Larger events approaching Mw 9
cannot reasonably be achieved for an island only about ~100 km x 100 km in size.
Further, the tsunamigenic zone for such an event is limited to the submarine portion of
the fault near the coast.
[17] An earthquake source on the south Kona coast would direct a tsunami at a 45°
angle to the azimuth to Kaua‘i. Tsunami modeling [Cheung, 2010] of a south Kona
event—using a Kalapana-style earthquake source—yielded tsunami amplitudes at Kaua‘i
only about 3 times greater than those from the Kalapana source region. Although it is
conceivable that a Kalapana-style earthquake on a 50-km fault along the north Kona
region of the Big Island could direct larger tsunami energy toward Kaua‘i, the
shallowness (<1500 m) of the coastal water will limit the tsunami height compared with
Kalapana and South Kona source regions. To accept this hypothesis, there should be
contemporaneous evidence of larger run-ups on the closer islands and the Big Island.
[18] There have been submarine landslides associated with Kaua‘i with estimated ages
at ~3.8 to 5 Ma [Keating, 1987; McMurtry et al., 2004]. Such an event is capable of
generating a local tsunami sufficiently large as to inundate the Kaua‘i sinkhole.
However, there is no compelling evidence for giant submarine landslides in the Hawaiian
Islands in the past 10,000 yrs [McMurtry et al., 2004]. Nonetheless, a smaller, local
submarine landslide at the Southeastern coast of Kaua‘i could possibly create a large
local tsunami deposit. To corroborate this hypothesis, additional data are required. First,
there should be evidence in the offshore bathymetry. Secondly, for a local Kaua‘i
submarine landslide, we may not expect large run-ups elsewhere in the Hawaiian Islands.
Therefore, a principal confirmation for an Aleutian source for the Kaua‘i deposit will be
paleotsunami evidence elsewhere in the State, such as the Kawainui marsh in Kailua on
Oahu, or in Waipio Valley of the Big Island. Lacking such confirmation, a closer review
of the Kaua‘i bathymetry may be required to confirm the local submarine landslide
source. In Hawai‘i we do not have a basic understanding of the rate of tsunamigenic,
local submarine landslides in the past thousands of years.
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[19] Finally, asteroid impacts will generate tsunamis. Recent estimates [Chesley and
Ward, 2006] suggest that the chances are about 1 in 70 million/year that a given generic
coastal point in the ocean will experience an asteroid (>300 m diameter) tsunami with
>10 m near-shore heights. The most probable impact-generated tsunamis have near-
shore heights <10 m and derive from asteroids 100–400 m diameter. For example, a
bolide 400 m in diameter striking the ocean at 12 km/s at 1000 km off the California
coast will produce tsunami run-ups of only about 5 m in Hawaii [Chesley and Ward,
2006]. Therefore, whereas the Kaua‘i paleotsunami deposit could have been caused by a
bolide impact within about 2000 km from the Island, there also is no evidence supporting
the hypothesis.
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Tables
Table S1. Faulting parameters are shown for earthquakes modeled in tsunami forecasts at the Kaua‘i sinkhole.
Earthquake Mw Uniform Fault
Slip, m Region (Figure 2)
SIFT subfaults*, fault length and area
Mw 9.25 ‡ 35 m East Aleutians ac18-23ab 600 km, 60,000 km2
Mw 9.25
35 m Alaska Peninsula ac26-31ab 600 km, 60,000 km2
Mw 9.25 35 m Quasi-1957
ac12-17ab 600 km, 60,000 km2
Mw 9.25 35 m Quasi-Kamchatka ki2-7ab 600 km, 60,000 km2
Mw 9.25ab ‡ (50-20m)
50 m (b), 20 m (a) 35 m average
East Aleutians ac18-23ab 600 km, 60,000 km2
Mw 9.29ab ‡ (50-20m)
50 m (b), 20 m (a) 35 m average
East Aleutians ac18-24ab 700 km, 70,000 km2
Mw 9.43 ‡ 35 m 1957, East Aleutians, 1946, Shumagin,
ac16-26ab 1100 km, 110,000 km2
Mw 9.45 ‡
35 m 1957, East Aleutians, ac13-24ab 1200 km, 120,000 km2
Mw 9.6 ‡ 35 m East Aleutian, 1946, Shumagin, 1938
ac18-31ab, ac21-31z 1400 km, 195,000 km2
*Each subfault has a unique identification code and corresponding location, fault geometry, and depth—see Gica et al., [2008] and its appendices. For example, ac18-23b refers to "Aleutian-Cascadia" subfaults 18 through 23, tier b (along the trench), which is 600 km long and 50 km wide. Tiers a, z, and y are subfaults successively further from the trench, and deeper. The fault width varies with the number of 50-km-wide subfault tiers incorporated in the earthquake. Earthquake Mw corresponds with a rigidity of 44 GPa for PREM. All events are modeled as pure thrust mechanisms. ‡Tsunami forecasts from these events inundated the Kaua‘i sinkhole. Note that all events including the eastern Aleutian segment caused inundation.
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Table S2. Faulting parameters for earthquakes located in eastern Aleutians with decreasing average displacements and Mw for a fixed fault area.
Earthquake Mw Uniform Fault
Slip, m Region (Figure 2)
SIFT subfaults*, fault length and area
Mw 9.25 ‡ 35 m East Aleutians ac18-23ab 600 km, 60,000 km2
Mw 9.2 30 m East Aleutians ac18-23ab 600 km, 60,000 km2
Mw 9.15 25 m East Aleutians ac18-23ab 600 km, 60,000 km2
Mw 9.1 20 m East Aleutians ac18-23ab 600 km, 60,000 km2
Mw 9.05 17.5 m East Aleutians ac18-23ab 600 km, 60,000 km2
*same as Table S1. All events are modeled as pure thrust mechanisms. ‡Tsunami forecasts only from this event inundated the Kaua‘i sinkhole.
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Figures.
Figure S1. The Makauwahi sinkhole, on the side of a lithified calcareous sand dune, is
viewed toward the southeast from an apparent altitude of 342 m. Inset photos show two
of the wall edges, indicating the edges of the sinkhole. Small white star in left inset
indicates location of north cave in Figure S3. The east wall (left) is 7.2 m above mean sea
level, and about 100 m from the ocean. Note for scale the people in the right image.