The California Tsunami of 15 June 2005 along
the Coast of North America
Alexander B. Rabinovich1, 2, Fred E. Stephenson3
and Richard E. Thomson1*
1Department
of Fisheries and Oceans, Ocean Sciences Division
Institute of Ocean Sciences
9860 West Saanich Road, Sidney BC V8L 4B2
2Russian
Academy of Sciences, P.P. Shirshov Institute of Oceanology, Moscow Russia
3Department
of Fisheries and Oceans, Canadian Hydrographic Service
Institute of Ocean Sciences, Sidney BC
[Original manuscript received 17 February 2006; in revised form 18 May 2006]
ABSTRACT An Mw = 7.2 earthquake occurred on 15 June 2005 (UTC) seaward of northern California off the west
coast of North America. Based on the earthquake location and source parameters, the West Coast and Alaska
Tsunami Warning Center issued a tsunami warning for the region extending from the California-Mexico border
to northern Vancouver Island, British Columbia (the first tsunami warning for this region since the 1994 Mw =
8.2 Shikotan earthquake). Six tide gauges on the west coast recorded tsunami waves from this event, with a maximum trough-to-crest wave height of 27.7 cm observed at Crescent City, California. Waves of 2.5 to 6.5 cm were
measured at the five other sites: Port Orford (Oregon), North Spit and Arena Cove (California), and Tofino and
Bamfield (British Columbia). The open-ocean Deep-ocean Assessment and Reporting of Tsunami (DART) buoys,
46404 and 46405, recorded tsunami waves of 0.5 and 1.5 cm, respectively, closely matching wave heights derived
from numerical models. Incoming tsunami wave energy was mainly at periods of 10 to 40 min. The observed
tsunami wave field is interpreted in terms of edge (trapped) and leaky (non-trapped) waves and a “trapping coefficient” is introduced to estimate the relative contribution of these two wave types. Due to the high (3000 m) water
depth in the source area, approximately two-thirds of the total tsunami energy went to leaky wave modes and only
one-third to edge wave modes. The improved response to and preparedness for the 2005 California tsunami compared to the 1994 Shikotan tsunami is attributable, in part, to the operational capability provided by the openocean bottom-pressure recorder (DART) system, higher quality coastal tide gauges, and the effective use of
numerical models to simulate real-time tsunamis.
RÉSUMÉ [Traduit par la rédaction] Un tremblement de terre de Mw = 7,2 s’est produit le 15 juin 2005 (UTC)
au large de la côte ouest de l’Amérique du Nord, à peu près à la latitude du nord de la Californie. En se basant
sur les paramètres de position et d’origine du séisme, le West Coast and Alaska Tsunami Center a émis une alerte
au tsunami pour la région s’étendant de la frontière Californie-Mexique jusqu’au nord de l’île de Vancouver, en
Colombie-Britannique (la première alerte au tsunami pour cette région depuis le séisme de Shikotan de Mw = 8,2
en 1994). Six marégraphes sur la côte ouest ont enregistré les vagues du tsunami lors de cet évènement; une hauteur
maximale de 27,7 cm de creux à crête a été observée à Crescent City, en Californie. Des vagues de 2,5 à 6,5 cm
ont été mesurées aux cinq autres sites de mesure: Port Orford (Oregon), North Spit et Arena Cove (Californie)
et Tofino et Bamfield (Colombie-Britannique). Les bouées DART (Deep-ocean Assessment and Reporting of
Tsunami) 46404 et 46405 de haute mer ont enregistré des vagues de tsunami de 0,5 et 1,5 cm, respectivement,
ce qui correspond de près aux hauteurs de vagues dérivées des modèles numériques. L’énergie des vagues de
tsunami à l’arrivée avait principalement des périodes de 10 à 40 min. Le champ de vagues du tsunami est interprété
en fonction des vages de bord (piégées) et des vagues de fuite (non piégées) et d’un « coefficient de piégeage »
introduit pour estimer la contribution relative de ces deux types de vagues. Étant donné la grande profondeur de
l’océan (3000 m) dans la région d’origine, environ les deux tiers de l’énergie totale du tsunami s’est retrouvée
dans les modes de vagues de fuite et seulement un tiers dans les modes de vagues de bord. La préparation et la
réponse améliorées au tsunami de la Californie en 2005 comparativement au tsunami de Shikotan en 1994 est en
partie attribuable à la capacité opérationnelle fournie par le système d’enregistrement de la pression au plancher
océanique en haute mer (DART), à des marégraphes côtiers de meilleure qualité et à l’utilisation efficace des
modèles numériques pour simuler les tsunamis en temps réel.
*Corresponding author’s e-mail: [email protected]
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1 Introduction
The 15 June 2005 earthquake occurred at 02:51 UTC (19:51
local time, PDT, on 14 June) with its epicentre at 41.28°N,
125.98°W (United States Geological Survey (USGS)),
approximately 145 km north-west of North Spit (Eureka),
California (CA) (Fig. 1). The magnitude of this earthquake
was initially estimated to be Mw = 7.4, but later corrected to
Mw = 7.2 (USGS; California Integrated Seismic Network
(CISN)). Based on the earthquake’s location and magnitude,
the West Coast and Alaska Tsunami Warning Center
(WC/ATWC) in Palmer, Alaska issued a tsunami warning for
all coastal areas from the California-Mexico border to Cape
Scott at the north end of Vancouver Island. This warning was
issued at 02:56 UTC, roughly 5 min after the main shock. In
British Columbia, the message was received by the Provincial
Emergency Program (PEP), which initiated a tsunami
response. Within 30 min of the initial warning, 26 communities
on the west coast of Vancouver Island were contacted to ensure
that they were implementing their emergency response plans.
Immediately following the earthquake, Vasily Titov of the
Pacific Marine Environmental Laboratory (PMEL) in Seattle
utilized a prototype model of the National Oceanic and
Atmospheric Administration (NOAA) Tsunami Forecast
System to predict tsunami amplitudes at five Deep-ocean
Assessment and Reporting of Tsunami (DART) stations in
the north-east Pacific. Results from the model were sent to the
International Tsunami Information Center (ITIC) Tsunami
Bulletin Board at 03:16 UTC (20:16 PDT), roughly 25 min after
the earthquake. The tsunami heights at DART buoys 46404
and 46405 (those closest to the epicentre) were predicted to
have amplitudes less than 1.5 cm. (See González et al. (2005)
for a description of the DART buoys and Titov et al. (2005b)
for a discussion of the real-time tsunami forecasting model.)
Tide stations along the west coast of the United States and
Canada were subsequently monitored for evidence of a tsunami wave. Only small tsunami waves were observed at coastal
sites and DART buoys. Based on this information, the
WC/ATWC determined that a destructive tsunami had not
been generated and cancelled the tsunami warning at 04:09
UTC, 15 June (21:09 PDT, 14 June).
Despite cancellation of the warning, the Canadian
Hydrographic Service (CHS) continued to monitor six tide
stations along the outer British Columbia coast and detected
weak (~4 cm) tsunami waves at two stations: Tofino and
Bamfield. The estimated tsunami arrival (ETA) at Tofino of
04:57 UTC (21:57 PDT) was in good agreement with the
observed arrival time of 04:51 UTC. Further examination of
tide gauge data also allowed us to identify a tsunami signal at
several California and Oregon stations closest to the earthquake epicentre (Fig. 1). In particular, a pronounced tsunami
wave arrived at Crescent City at 03:37 UTC (46 min after the
main shock) and, following resonant amplification, eventually reached a maximum observed trough-to-crest wave height
of 27.7 cm. The tsunami waves generated by the California
earthquake were also recorded by two DART buoys, 46404
and 46405, located in the vicinity of the epicentre (Fig. 1).
The purpose of the present study is to examine the statistical (including spectral) characteristics of the tsunami waves
generated by the 15 June 2005 California earthquake, and to
compare these characteristics with those of other tsunamis
recently recorded in this region. We also discuss problems
relevant to tsunami preparedness for the British Columbia
coast.
2 Tsunami observations
The ability to detect tsunami waves in a tide gauge record
depends strongly on the signal-to-noise ratio. For weak tsunami signals, wave detection is a major challenge. Due to the
better quality of modern instruments, digital recording, smaller sampling intervals and higher accuracy, we can now identify much smaller tsunamis than was previously possible.
Reliable statistics for weak tsunamis will likely advance our
understanding of tsunami physics and generation mechanisms
and, as a result, improve tsunami warnings and mitigate the
catastrophic consequences of tsunami waves.
Processing tide gauge data begins with a preliminary analysis involving de-tiding, and low-pass and high-pass filtering
to reduce the background noise level, thereby improving the
tsunami signal-to-background noise ratio. Low-pass filtering
is especially important when infragravity (IG) waves are present in the data. Generated by non-linear interaction of wind
waves and swell (see Holman et al., 1978; Battjes, 1988), IG
waves adversely affect our ability to detect tsunamis, especially during storm conditions. Typical periods of IG waves
are from 30 to 300 sec, although on stormy days these waves
may have much longer periods (up to 35–40 min; Kovalev
et al. (1991)). To address data processing problems associated with these waves, we follow the approach discussed by
Rabinovich et al. (2006) in connection with the 2004 Sumatra
tsunami identified in the North American tide gauge records.
a Coastal British Columbia Observations
The destructive tsunamis between 1992 and 1998 in the
Pacific Ocean led to a major upgrade of the existing tsunami
warning and Permanent Water Level Network (PWLN) stations on the coast of British Columbia. The new digital instruments were designed to measure sea level variations
continuously with 1-minute sampling. During the period
1999–2004, long time series of high quality 1-minute sea
level data were collected and several weak tsunamis were
recorded (Rabinovich and Stephenson, 2004). For example,
the 2004 Sumatra tsunami was identified at six tide gauges,
which are located mainly on the outer coast of British
Columbia: Victoria, Bamfield, Tofino, Winter Harbour, Port
Hardy and Bella Bella (Rabinovich et al., 2006). Records from
these stations, plus Langara (located on the northern coast of
the Queen Charlotte Islands), were subsequently examined for
possible tsunami waves associated with the California earthquake of 15 June 2005. All records were de-tided and then
high-pass filtered with a 3-hour Kaiser-Bessel window.
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Fig. 2
High-passed records of the California tsunami of 15 June 2005 at
two stations (Tofino and Bamfield) located on the coast of
Vancouver Island (BC). The dashed vertical line labelled “E”
denotes the time of the main earthquake shock (Mw = 7.2); “ETA”
is the estimated tsunami arrival time at station Tofino.
waves persisted for about four hours and had maximum
trough-to-crest wave heights of 4.3 cm. (Tsunami signals
were also identified in the gauge records for Winter Harbour
and Port Hardy, but they were < 1 cm.) We speculate that the
more regular train of waves was associated with edge waves
(see Section 3).
Fig. 1
Map of the north-east Pacific showing the location of the Mw = 7.2
California earthquake epicentre of 15 June 2005 (star), and the
positions of the six selected tide gauges and two DART buoys that
recorded the tsunami waves. The dashed lines are calculated 15min isochrones of tsunami travel time from the source area.
(Abbreviations are BC-British Columbia; WA-Washington; OROregon; CA-California.)
The tsunami signal was clearly detected at Tofino and
Bamfield (Fig. 2), with an observed tsunami arrival (TA) time
of 04:51 UTC for the Tofino record (Table 1), in good agreement with the estimated arrival time (ETA) of 04:57 UTC
(20:57 PDT) (compare with the predicted arrival times in Fig. 1).
The first observed wave was negative and had a trough-tocrest height of 3.3 cm. A few minutes later, at 04:56 UTC, a
tsunami wave (also negative) arrived at Bamfield with a wave
height of 1.8 cm; the maximum wave height at Bamfield (the
third wave) was 2.6 cm. The distance between the source
area and these sites in British Columbia is approximately
850–980 km, corresponding to a mean tsunami propagation
speed of 425–490 km hr–1.
The first tsunami waves to arrive at Tofino were irregular
but were followed 1 hour later by a train of regular waves
with typical periods of around 22 min (Fig. 2). The regular
b Near-Field Coastal Observations
In addition to the British Columbia records, we also examined
records from four coastal tide gauges closest to the epicentre
area: Port Orford (Oregon), Crescent City (California), North
Spit (California), and Arena Cove (California) (Fig. 1). All
records had 1-minute sampling. Regrettably, the records for
the North Spit and Arena Cove stations are very noisy due to
high-frequency oscillations associated with IG waves. To
improve the signal-to-noise levels for these two stations, we
used a low-pass filter on the time series with a 6-minute
Kaiser-Bessel window. To suppress low-frequency oscillations associated with atmospheric activity, the de-tided
records for all four stations were also processed with a highpass filter with a 3-hour Kaiser-Bessel window (Emery and
Thomson, 2003). These filtered series (Fig. 3) were used to
estimate tsunami characteristics (Table 1).
At Crescent City, the first wave was negative (trough). The
maximum trough-to-crest wave height (27.7 cm) was associated with the third wave (Fig. 3). Tsunami oscillations at this
station were near monochromatic and had a period of about
22 min. Tsunami waves with a similar period were observed
at this site following the 2004 Sumatra earthquake
(Rabinovich et al., 2006). At three other stations, Port Orford,
North Spit and Arena Cove, tsunami waves from the 2005
California event were only around 4.0–6.5 cm (Table 1). At
all four stations the first recorded tsunami wave was negative.
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TABLE 1.
Observed properties of tsunami waves generated by the Mw = 7.2 California earthquake of 15 June 2005.
Station
Tofino, BC
Bamfield, BC
Port Orford, OR
Crescent City, CA
North Spit, CA
Arena Cove, CA
DART 46404
DART 46405
Arrival time (UTC)
04:51
04:56
03:47
03:37
03:19
03:49
03:44
03:29
Travel time (min)
First wave sign
Maximum wave height (cm)
negative
negative
negative
negative
negative
negative
negative
positive
4.3
2.6
4.0
27.7
4.7
6.5
0.53
1.45
120
125
56
46
28
58
53
38
c DART Observations
Tsunami waves generated by the California earthquake were
recorded by two DART buoys, 46404 and 46405, located in
the vicinity of the earthquake epicentre (Fig. 1). Both instruments also recorded seismic surface Rayleigh waves that
arrived at DART 46405 at approximately 02:53:15 UTC (i.e.,
about 2 min 21 s after the main shock) and at DART 46404 at
about 02:53:45 UTC (2 min 51 s after the main shock).
Rayleigh waves at the DART sites preceded tsunami wave
arrivals at these sites by roughly 36 min and 50 min, respectively. The ground oscillations ranged from -11 to +4.5 cm at
DART 46405 and -1 cm to +1 cm at DART 46404 (Fig. 4).
Sufficiently strong Rayleigh wave oscillations at DART
buoys 46405 and 46404 initiated an automatic alarm and subsequent transmission of data to the tsunami warning centres
every 15 seconds.
As predicted by the preliminary NOAA model computation
(Vasily Titov, personal communication, 2005), the observed
tsunami waves at the DART locations were quite small. The
first tsunami wave to hit DART 46405 – a positive wave with
a height of +0.78 cm – arrived at 03:28:45 UTC, about 38 min
after the main shock. The first wave to hit DART 46404 – a
negative wave with a height of –0.38 cm – at 03:43:45 UTC,
arrived about 53 min after the main shock. Maximum troughto-crest wave heights were 1.45 cm at DART 46405 and
0.53 cm at DART 46404 (Table 1). Based on the DART
observations, the NOAA tsunami model was adjusted (Fig.
4). This, in turn, yielded a revised earthquake magnitude of
Mw = 7.2, rather than the first seismically derived magnitude,
Mw = 7.4. Subsequently improved seismological estimates
confirmed the earthquake magnitude to be Mw = 7.2.
3 Influence of edge and leaky waves
Our analysis of the sea level records suggests that coastal
topographic effects played an important role in the observed
propagation and response of the 2005 California tsunami.
Ignoring alongshore variations in topography, sea level displacements associated with tsunamis propagating near the
coast have the form
η( x , y; t ) = ζ( x )ei (ω t − ky) ,
23
17
17, 60
22
28, 50
9, 14
22
20
cross-shore depth profile h = h(x) yield the following equation
for the cross-shore structure of sea level displacement, ζ(x):
ζ "( x ) +
 ω2

h '( x )
− k 2  ζ( x ) = 0
ζ '( x ) + 
h( x )
 gh( x )

(2)
(LeBlond and Mysak, 1978). The condition of no mass flux
through the coastal boundary requires that
h( x )ζ '( x ) = 0 at x = 0
(3)
where h(0) = h0 (a non-zero constant) and ζ′ ≡ d/dx. Equations
(2)–(3) describe two types of waves (Munk et al., 1964;
Rabinovich, 1993):
(1) Trapped edge waves (Stokes waves) that propagate
alongshore and decay away from the coast such that
ζ( x ) → 0 at x → ∞ .
(4)
For a given frequency or wavenumber, edge waves
have a discrete spectrum associated with a set of normal modes. If we assume that the open ocean depth is
uniform, h(x) = H at x → ∞ , then in the dispersion diagram (ω,k) all edge wave modes lie within the area:
ω 2 / gh0 > k 2 > ω 2 / gH ;
(5a)
c0 = gh0 < c < gH = c∞ ,
(5b)
where c=ω /k is the alongshore wave phase speed.
(2) Non-trapped leaky waves that can arrive at the shelf
from the open ocean and then radiate back after
reflection from the shelf and coastline. These waves
have a continuous spectrum filling up the sector
0 ≤ k 2 < ω 2 / gH
(1)
where x and y are Cartesian coordinates in the cross-shore and
alongshore directions, ω (> 0) is the angular frequency, and k
is the alongshore wavenumber. The linearized, long-wave
barotropic equations for free waves propagating alongshore in
a non-rotating coordinate system with a uniform monotonic
Period(s) (min)
(6)
of the ω,k -diagram. Any point of this sector is a solution
of Eq. (2) with a boundary condition given by Eq. (3). In
contrast to edge waves, leaky waves have a cross-shore
component, l, of the wavenumber vector κ = {l,k} and
propagate with a longwave speed c = ω/κ = √gh(x),
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California Earthquake of 15 June 2005 (Mw = 7.2)
Time (UTC hours)
Fig. 4
Time (UTC hours)
Fig. 3
High-passed records of the California tsunami of 15 June 2005 at four
stations located on the coast of Oregon (Port Orford) and California
(Crescent City, North Spit and Arena Cove). The dashed vertical
line labelled “E” denotes the time of the earthquake (Mw = 7.2).
where κ = √l2+k2 . Leaky waves do not have discrete
modes but occupy distinct frequency bands for which
there is amplification of incoming waves (“shelf resonance”) in the sense of an open organ-pipe response
(Munk et al., 1964). The importance of edge waves to
tsunami propagation was first demonstrated by Miller
et al. (1962) who showed that long-duration (~one
week) ringing of tsunami waves for the entire coast of
North America after the 1960 Chile earthquake was
associated with such wave motions.
Kajiura (1972) discussed the generation of tsunami waves
by seafloor deformation and showed that the tsunami energy
generated during this process is transformed into two wave
types: edge waves trapped over the shelf and non-trapped
(leaky) waves that radiate tsunami energy back into the open
ocean. This is consistent with González et al. (1995) who
observed earthquake-generated leaky and edge waves along
the California coast following the 1992 Cape Mendocino
tsunami. Leaky waves were responsible for the first tsunami
waves observed on the coast, while edge waves were responsible for most of the tsunami energy and maximum wave
heights observed on the coast. In contrast to edge waves,
which decay slowly as they propagate along the continental
Surface ground Rayeigh waves (RW) and tsunami waves recorded
on 15 June 2005 at two open-ocean DART buoy stations located
off the Pacific coast of the United States (locations of the buoys
are shown in Fig. 1). “TA” is the observed tsunami arrival time
and the dashed vertical line labelled “E” indicates the time of the
main shock. Tsunami waves numerically simulated by Vasily
Titov (PMEL/NOAA, Seattle) are shown for DART 46405.
margin, the faster propagating leaky waves decay quickly
(roughly as the square root of the off-source distance) as their
energy is spread to the open ocean. As a consequence, edge
waves are expected to dominate at sites far away from the
source area.
Kajiura (1972) further showed that the ratio of edge to
leaky wave energy depends strongly on the offshore distance
of the tsunami source region: the nearer the source to the
coastline, the greater the rate of the trapped edge wave energy and the lower the rate of energy radiation into deep water.
Following Rabinovich (1993), the relative importance of
these two types of waves may be estimated using simple wave
reflection constraints. Analogous to optical ray tracing, the
angle ϕ∞ of a leaky wave incident upon the shelf from the
open ocean may be presented as
sin ϕ ∞ = k∞ / κ ∞ = k∞ c∞ / ω ,
(7)
where κ∞ is the magnitude of the open ocean wavenumber
vector κ of the leaky waves, k∞ is the alongshore component
of this vector, and c∞= √gH is the open ocean phase speed of
these waves. The angle ϕ∞ = 0° corresponds to waves arriving
normal to the shelf, while angles ϕ∞ = ±90° correspond to
waves propagating parallel to the shelf. Snell’s law (LeBlond
and Mysak, 1978) for a step-like shelf
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H at x > L;
h(x) =
h0 at L ≥ x ≥ 0,
(8)
gives, for angle ϕ0 on the shelf,
c
sin ϕ 0
= 0 =
sin ϕ ∞ c∞
gh0
gH
= ε0 ,
(9a)
where ε0 = √h0 / H. Equation (9a) may be generalized for an
arbitrary cylindrical depth profile using multiple step functions
(Rabinovich, 1993) such that, for each jth step (independent of
the number of intermediate steps),
sin ϕ j
sin ϕ ∞
=
cj
c∞
=
gh j
gH
= εj ,
(9b)
whereby the incidence angle, ϕ, depends only on the open
ocean depth, H, and local depth, hj.
An important consequence of Snell’s law is that any ocean
wave impinging on an ideal shelf (one with perfect reflection and
no dissipation or scattering) at arbitrary angle –90° < ϕ∞ < 90°,
after multiple reflections from the coast and shelf border, will
radiate back to the open ocean. For perfect reflection, all of
the incoming wave energy is reflected from the shelf region
back into the deep ocean (Fuller and Mysak, 1977). This
means that the trapped (edge) waves observed on a uniform
shelf region cannot be generated by waves arriving from the
open-ocean but must originate from waves propagating along
the shelf. According to Snell’s law, there is a critical angle for
a wave propagating along the shelf (Rabinovich, 1993):
ϕ crit = sin −1 ε ,
(10)
such that if  ϕj < ϕjcrit this wave component, " j", will
escape from the shelf and propagate into the open ocean. On
the other hand, if  ϕj > ϕjcrit the wave will be reflected from
the shelf-break and therefore trapped over the shelf analogous
to an internal reflection in an optical wave guide. Thus, if the
generation source (e.g., earthquake epicentre) is located over
the shelf, then depending on the initial angle, we find
– ϕjcrit < ϕj < ϕjcrit → leaky waves
90° > ϕj > ϕjcrit → edge waves.
(11)
(These expressions are written for wave angles –90° < ϕ∞ < 90°,
however, similar expressions may be presented for
90° < ϕ∞< 270°.)
If we assume that the initial source is isotropic, we can
introduce two coefficients: Radiating coefficient
Cradiat =
2ϕ crit 2 sin −1 ε
=
,
π
π
(12)
indicating what proportion of the initial source energy radiates into the open ocean (directly or after perfect reflection
from the shelf and coastline); and Trapping coefficient
Ctrapped = 1 −
2ϕ crit
2 sin −1 ε
= 1−
= 1 − Cradiat,
π
π
(13)
giving the proportion of energy trapped on the shelf. The radiating and trapped coefficients determine the relative contribution of leaky and edge waves in the tsunami wave field.
Equations (12) and (13) clearly demonstrate that the closer
the source to the shore (i.e., the shallower the water depth at
the source area), the greater the energy going into edge waves
and the lower the energy going into non-trapped (leaky)
waves, in agreement with Kajiura (1972).
The epicentre of the 2005 California earthquake was
located on the California continental slope, at a mean
depth of about 3000 m. The open ocean depth in this
region is roughly 4000 m. From Eq. (10), the critical angle
ϕcrit = sin–1[(3000/4000)1/2] = π/3 = 60°. Thus, according to
Eqs (12) and (13), about two-thirds of the total tsunami energy went to non-trapped leaky modes and only one-third to
edge waves. For comparison, the mean depth in the source
area of the 1992 Cape Mendocino tsunami was about 1000 m,
so the critical angle was 30º and the relation between leaky
and edge waves had the opposite ratio (one-third and twothirds, respectively). These estimates are in good agreement
with González et al. (1995) who found that edge waves dominated the sea level records for the Cape Mendocino tsunami.
The relatively small amount of edge wave energy in the
2005 California tsunami is one of the reasons why these
waves were not observed at the four US stations located in the
vicinity of the source (Fig. 3). Another reason is that, according to Eq. (11), the angle sectors of edge and leaky waves
associated with the California tsunami were as follows:
60° < ϕ j < 120°,
edge waves → 
240° < ϕ j < 300°;
−60° < ϕ j < 60°,
leaky waves → 
120° < ϕ j < 240°.

(14)
Based on these results, tsunami energy in the form of edge
waves radiated northward and southward from the source,
leaving the near-source region in a wave “shadow” region. In
contrast, leaky waves travelled seaward and shoreward. As a
result, tsunami waves recorded at Port Orford, Crescent City,
North Spit and Arena Cove (Fig. 3) were likely due to leaky
waves and to local seiche oscillations generated by arriving
leaky waves.
The situation is different for the two Canadian stations,
Tofino and Bamfield (Fig. 2). As mentioned in Section 2a, the
first tsunami waves arrived at Tofino at 04:51 and at Bamfield
at 04:56 UTC (Table 1), in good agreement with the estimated
arrival time of 04:57 UTC. Because edge waves propagate
much more slowly than leaky waves, the first arrivals were
likely leaky waves that had propagated in the open ocean with
a mean speed of 425–490 km hr–1 (Fig. 1). The first irregular
waves that followed about one hour later (~05:58 UTC) are
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more likely to have been a train of edge-like waves with characteristic periods of approximately 22 min. As a rough
approximation, the phase speed of the nth mode edge wave is
(using LeBlond and Mysak, 1978):
cn =
ωn
gT
g
= (2n + 1)
tan β = (2n + 1) n tan β ,
k
ωn
2π
(15)
where ωn= 2π/Tn is the angular frequency of the mode,
h(x)/x = tan β is the slope of the shoreline in the seaward (x)
direction, and β is the slope angle. For tan β = 0.02 and period
T = 22 min, the fundamental mode (n = 0) has a phase speed
of c0 ≈ 150 km hr–1 and requires about six hours to reach
Tofino from the source area. The observed train of regular
waves reached Tofino approximately three hours after the
earthquake, about one hour later than estimated for leaky
waves propagating in the deep ocean and about three hours
earlier than predicted for edge waves. This discrepancy
implies a fundamental disagreement between observation and
the classical theory of boundary waves that may be related to
imperfect wave reflection and energy exchange between
leaky and edge waves. In particular, Fuller and Mysak (1977)
demonstrated that, for an irregular coast and bottom topography, scattering effects can lead to a flux of energy from incident leaky waves into coastally trapped edge waves.
Specifically trapped edge waves can be generated by a tsunami striking an irregular coast. These trapped waves can be
quite significant. The scattered fraction of incident power flux
is about 50%. For the Tofino and Bamfield sites, major topographic scattering features include the entrance to Juan de
Fuca Strait and the La Perouse Bank region of southern
Vancouver Island. Tsunami waves from the 2005 California
tsunami would have arrived at this region in approximately
two hours (Fig. 1). The distance from the strait entrance to
Tofino is around 150 km, or about one hour of idealized edge
wave propagation time. The combined travel time of about
three hours is in good agreement with observation.
4 Time-frequency analysis
To examine temporal variations in the frequency of the
observed California tsunami waves, we used a method developed by Dziewonski et al. (1969) to study non-stationary seismic signals in which the time series displays rapid temporal
changes in amplitude and/or phase. The method, which is
similar to wavelet analysis (Emery and Thomson, 2003), is
based on narrow-band filters, H(ω), with a Gaussian window
that isolates a specific centre frequency, ωn=2πƒn:
H n (ω ) = e
 ω −ωn 
–α 

 ω 
2
.
(16)
The frequency resolution is controlled by the parameter α.
The higher the value of α, the better the resolution in the frequency domain, but the poorer the resolution in the time
domain (and vice versa). This means that, if we are interested
in the timing of a specific event (for example, estimation of
the tsunami wave arrival), we need to reduce α. However, if
we are interested in the frequencies of observed wave trains,
we need to increase α. For most of our computations, we used
α = 60 (Fig. 5), but also tried smaller values to decrease the
uncertainty in identifying the wave arrival times.
A system of Gaussian filters leads to a constant resolution
on a scale. The Fourier transform of Hn(ω) is:
hn (t ) =
πω n
e
2α
− ω 2n tn2
4α
cos (ω n t ) .
(17)
Demodulation of a sea level time series, ζ(ωn;t), yields a
matrix of amplitudes (phases) of wave motions with columns
representing time and rows representing frequency (the socalled f-t diagrams). This method can be used effectively to
indicate how the tsunami wave energy E(f,t) changes as a
function of frequency, f, and time, t (González and Kulikov,
1993; Rabinovich et al., 2006).
Figure 5 presents f-t diagrams for six coastal tide gauge
locations (Fig. 1). The plots reveal a complicated co-existence
of longwave oscillations originating from both incoming
tsunami waves and atmospherically induced seiches. In most
of the plots, tsunami arrival times are well-defined and mutually consistent. In the Bamfield, Port Orford and Crescent
City tide gauge records, tsunami wave periods range mainly
from 12 to 30 min, with dominant periods of 17–25 min.
According to the f-t diagram, the Crescent City gauge recorded a train of tsunami waves with a duration of approximately
eight hours and a peak period of 22 min. This is the same period observed in the background seiche oscillations preceding
the tsunami waves (Figs 3 and 5) and in tsunami oscillations
at this site arising from the 2004 Sumatra tsunami
(Rabinovich et al., 2006). It would appear that the 22 min
oscillations represent the fundamental (Helmholtz) mode for
the Crescent City harbour.
The f-t diagram for North Spit reveals an increase in longwave energy at periods of 8 to 35 min, beginning approximately 30 min after the earthquake, in good agreement with
the predicted tsunami arrival time. Oscillations with periods
of 12 and 28 min are most prevalent (Fig. 5). As indicated by
the f-t diagram (and the record itself), there were also significant short duration, 50 min, oscillations associated with the
main shock. Similar oscillations are also evident in the record
and in the f-t diagram for Port Orford (Figs 3 and 5).
The marked temporal and frequency variability in the
Tofino and Arena Cove f-t diagrams indicate that the tsunami
waves had multiple origins at different frequencies. Arriving
tsunami waves at these sites were apparently superimposed
on existing oscillations. At Arena Cove, the tsunami waves
generated oscillations with periods of 9 and 14 min, and first
arrived about one hour after the main shock. At Tofino, tsunami waves appeared as oscillations with periods of 17 and 23
min (Fig. 5). We note that at some sites (e.g., at Bamfield and
Port Orford) the tsunami wave arrivals were difficult to identify in the original records (Figs 2 and 3) but easy to distinguish in their respective f-t plots. In contrast, at other sites
(e.g., Tofino), the tsunami wave arrivals were easier to identify in the original record than in the f-t plot.
ATMOSPHERE-OCEAN 44 (4) 2006, 415–427
Canadian Meteorological and Oceanographic Society
422 / Alexander B. Rabinovich et al.
Time (UTC)
Fig. 5
Time (UTC)
Frequency-time plots (f-t diagrams) for the 15 June 2005 California tsunami tide gauge records for Tofino (BC), Bamfield (BC), Port Orford (OR),
Crescent City (CA), North Spit (CA), and Arena Cove (CA). “E” indicates the time of the main shock and “TA” the observed tsunami arrival time.
5 Spectral analysis
The data from the six coastal tide gauges in Fig. 1 were spectrally analysed. To examine the spectral properties of tsunami
oscillations during the California tsunami of 15 June 2006,
and to compare these properties with those of the background
oscillations at the same sites, we separated the records into
two parts. The time period preceding the tsunami arrivals (17
hours for the two British Columbia stations and 13 hours for
the four United States stations) was identified as “normal”
and selected for analysis of background signals. For the
“tsunami” periods following the wave arrivals, we chose time
periods of 6.4 and 8.5 hr for the British Columbia and United
States stations, respectively. Our spectral analysis procedure
is similar to that described by Emery and Thomson (2003). To
improve the spectral estimates, we used a Kaiser-Bessel spectral window with half-window overlaps prior to the Fourier
transform. The length of the window was chosen to be
256 min, yielding 4 to 14 degrees of freedom per spectral esti-
mate depending on the length of the data segment. Figure 6
shows the results of the analysis for all six stations.
In general, the spectra of both tsunami and background are
“red”, with spectral energy decreasing with increasing frequency as ω–2. This is typical for longwave sea level spectra
(Aida et al., 1972; Kulikov et al., 1983; Rabinovich, 1993,
1997). At most stations, the difference between tsunami and
background spectra is small, demonstrating that the 2005
California tsunami was relatively weak while background
atmospherically induced oscillations were relatively strong.
The spectral peaks differ at each station (Fig. 6) indicating the
influence of local topographic effects. The most prominent
peak (period ~22 min) was observed at Crescent City; this
peak, which is the same for tsunami and background spectra,
is an indication of tsunami resonance at this site. At other sites
the main spectral peaks of tsunami and background oscillations are similar (Fig. 6). This result is in good agreement
with the well-known fact that periods of tsunamis are primarily
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The California Tsunami of 15 June 2005 along the Coast of North America / 423
Fig. 6
Spectra of background (pre-tsunami) and tsunami oscillations for the six tide gauge records shown in Figs 2 and 3. Periods (in minutes) of the main
spectral peaks are indicated.
related to resonant properties of the local and regional topography rather than to characteristics of the source, and are
almost the same as those of ordinary (background) long
waves for the same sites. For this reason, the spectra of
tsunamis from different earthquakes are usually similar at the
same location (Honda et al., 1908; Miller, 1972; Rabinovich,
1997). It is therefore difficult to reconstruct the source
region spectral characteristics based on data from coastal
stations.
To separate the influences of the local topography and the
source, and to reconstruct the open-ocean spectral characteristics of the California tsunami of 15 June 2005, we used the
method of Rabinovich (1997). The method is based on the
assumption that the spectrum, S(ω), of sea level oscillations
near the coast can be represented as
ATMOSPHERE-OCEAN 44 (4) 2006, 415–427
Canadian Meteorological and Oceanographic Society
S(ω)=W(ω)E(ω) ,
(18)
424 / Alexander B. Rabinovich et al.
where ω is the angular frequency, W(ω) = H2(ω), H(ω), is the
admittance function describing the linear topographic transformation of long waves approaching the coast, and E(ω) is
the source spectrum. Using Eq. (18), we next assume that all
individual peculiarities of the observed spectrum, Sj(ω), at the
j th site are related to the site-specific topographic function
Hj (ω), while all general properties of this spectrum are associated with the source (assuming that the source is the same
for all stations). For typical background oscillations E(ω) =
S0(ω), where S0(ω) is the longwave spectrum in the open ocean.
Long-term bottom pressure measurements in various regions
of the Pacific Ocean (Kulikov et al., 1983; Filloux et al.,
1991) have demonstrated that the function S0(ω) in the deep
ocean is smooth and monotonic and almost universal. It may
be roughly described as
S0(ω) = Aω–2
(19)
where A = 10–3–10–4 cm2 cpm is a constant slightly dependent on atmospheric activity and individual properties of the
basin (see also Aida et al., 1972).
Sea level oscillations observed near the coast may be
presented as
ζobs(t) = ζt(t)+ζb(t) ,
(20)
where ζt are the tsunami waves generated by an underwater
seismic source and ζb are the background surface oscillations.
If the spectra of both tsunami and background oscillations
have the form of Eq. (18), we can compare these spectra to
separate the source and topographic effects. In this way, we
assume that the spectra of the observed tsunami and background long waves are a product of the same topographic
admittance function. This function is strongly variable in
space (due to the resonant properties of local topography) and
almost constant in time. Conversely, the corresponding
source function is spatially uniform, but varies considerably
with time.
It follows from Eq. (20) that the observed spectrum Sobs(ω)
may be presented as
Sobs(ω) = St(ω)+Sb(ω)
(21)
where St(ω) is the tsunami spectrum and Sb(ω) is the background spectrum. If we use Eqs (18) and (19) and assume that
the background noise is the same before and during the tsunami event, we obtain the expression:
R(ω ) =
Sobs (ω )  E (ω ) + S0 (ω ) 
=
≅ A−1ω 2 E (ω ) + 1 . (22)
Sb (ω )
S0 (ω )
The spectral ratio R(ω) is independent of local topographic
influence and determined solely by the external forcing (i.e.,
by characteristics of the open ocean waves). This “source
function”1 gives the amplification of the longwave spectrum
during the tsunami event relative to the background conditions.
Figure 7 presents the spectral ratios (source functions) for
the California tsunami for all six coastal tide gauge stations.
In contrast to the tsunami spectra (Fig. 6), the source functions
for the different sites are similar. For example, the source
functions for the Crescent City and Arena Cove records show
significantly more similarity than their spectra show.
According to these functions, the main energy of the external
forcing (associated with the spectral properties of the openocean tsunami source) was concentrated in the frequency
range 1.5 to 7.5 cph (periods from 8 to 40 min) with peak values in the ranges of 2.5–3.5 cph and 4.5–6.0 cph (periods
17–24 min and 10–13 min). Results confirm that close matching of the source frequencies with the fundamental frequency
of the Crescent City harbour is responsible for the observed
resonant amplification of tsunami oscillations at this site.
In general, the tsunami energy flux from a source area is
different for different directions of wave radiation, generating
different types of wave modes (Section 3). In particular, the
tsunami waves observed at Bamfield and Tofino (Fig. 2) were
apparently trapped edge waves that may have had a secondary
scattering source off the entrance to Juan de Fuca Strait, while
tsunami oscillations recorded in the vicinity of the seismic
source (Port Orford, Crescent City, North Spit and Arena
Cove) were likely associated with non-trapped leaky waves
and local seiche oscillations. Accordingly, the source functions constructed for these two groups of stations (Fig. 8)
should reflect these differences. For the northern (British
Columbia) group, the mean source function has major maxima at frequencies of 1.65 cph (36 min period) and 3.3 cph (18
min period) which likely represents tsunami energy focused
into two edge-wave modes. For the southern (California and
Oregon) group of stations, the source function lacks significant peaks and the tsunami energy is distributed more uniformly with frequency, with a gradual increase from low to
high frequencies and then an abrupt drop at a frequency of
6.7 cph (9 min period).
6 Tsunami preparedness
As noted earlier, the warning issued on 15 June 2005 was the
first tsunami warning for the coast of British Columbia since
the 1994 Mw = 8.2 Shikotan earthquake and tsunami
(Southern Kuril Islands). The detection and alert system has
changed profoundly since 1994. In 1994 there were very few
digital tide gauges in operation and no deep-ocean gauges to
provide a tsunami warning. The 1994 Shikotan earthquake
occurred on 4 October at 13:23 UTC, but it was not until 16:01
UTC that Bulletin 002 was issued indicating a 3.46 m wave at
Hanasaki, Japan. Bulletin 004 at 18:46 UTC indicated wave
heights of 0.15 m at Shemya, Alaska and 0.17 m at Wake
Island, and at 19:40 UTC, Bulletin 005 indicated a 0.50 m
wave at Midway Island. With the observed wave height at
Midway Island, there was concern over potentially destructive wave activity at Hawaii and elsewhere. It was not until
21:50 UTC that the Pacific Tsunami Warning Center (PTWC)
1 A source function defined in this way is always positive in contrast to R(ω) - 1, which can be negative at some frequencies because of temporal variations in
the background noise spectra.
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Fig. 7
Source functions of the California tsunami of 15 June 2005 reconstructed from the six tide gauge records shown in Figs 2 and 3.
issued Bulletin 006 indicating that the tsunami wave height at
Hilo, Hawaii had been only 0.50 m and the tsunami warning
was cancelled. For Hawaii, it was a false alarm. However, the
cost of this alarm was the loss of two human lives (one during the evacuation response and the other due to a heart
attack) and about US$30 million in economic loss.
On the British Columbia coast, the CHS network of tide
gauge stations used analogue recorders to measure water levels. Only the tsunami warning stations at Bamfield and
Winter Harbour were equipped with digital recorders, and
these instruments had to be remotely reset from the standard
15-min sample interval to a 1-min sample interval to provide
the high sample rate required for tsunami detection. The
tsunami wave measured 22.4 cm at Winter Harbour and
9.2 cm at Bamfield. Only recently have the analogue records
been inspected for evidence of the Shikotan tsunami. In addition to Bamfield and Winter Harbour, it has been determined
that Tofino, Port Alberni and Victoria also recorded the tsunami, with the largest wave being 23.7 cm at Port Alberni.
In 1994, the time between the earthquake and the cancellation of the tsunami warning was 8 hr 32 min. Why did it take
so long? The location and number of tide gauges able to provide water level information in real-time was a factor, and a
denser network of both coastal and deep ocean stations would
have been of great benefit. The initial scope of the tsunami
warning was too large and was in error; however, the lack of
a prediction model integrated with data from deep ocean
gauges also compounded the problem. In 2005, data for the
California tsunami were received from two DART buoys
within about 45 min of the earthquake and were used to validate the tsunami model predictions. The tsunami warning was
cancelled at 04:09 UTC, shortly after the first observed coastal
wave heights were obtained at Crescent City (California) and
DART Buoy 46405.
The first tsunami waves simulated operationally using
DART buoy data and the PMEL/NOAA tsunami forecast
model were waves for the Mw = 7.8 earthquake of 17
November 2004 on the shelf of the Rat Islands, Alaska (Titov
et al., 2005b). This tsunami was detected by three DART
buoys located south of the Aleutian Trench. The real-time
buoy data combined with the model database were used to
produce the real-time tsunami forecast for the Hawaiian
Islands before the non-destructive waves were able to strike
Hawaii. So this event was a genuine test indicating the applicability of the methodology to tsunami forecasting. The experience gained from the 2004 tsunami was used during the
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426 / Alexander B. Rabinovich et al.
Fig. 8
As in Fig. 7 but for two groups of stations: (a) two BC stations; and
(b) four OR and CA stations. Mean source functions are shown for
each group.
California tsunami of 15 June 2005 and was probably the first
tsunami to be simulated numerically while a tsunami warning
was in effect. The results of this simulation were used to predict tsunami wave heights at several coastal and DART buoy
locations. The small predicted heights were in good agreement with the observed wave heights. The signs of the recorded first wave, negative at coastal sites and positive at DART
46405, support the assumption that there was a seafloor drop
on the coastal side of the source and an uplift on the ocean
side.
7 Discussion and conclusions
Prior to 1990, the main threat to the west coast of the United
States and Canada was assumed to be from distant transPacific tsunamis such as the destructive 1960 Chilean tsunami and 1964 Alaska tsunami. The Mw = 7.1 Cape Mendocino
earthquake that occurred on 25 April 1992 offshore of northern California at the southern end of the Cascadia Subduction
Zone produced a modest local tsunami. That tsunami was
recorded at Port Orford, Crescent City, North Spit, Arena
Cove, Point Reyes and a few other sites along the west coast
of the United States (González et al., 1995), indicating that
the Cascadia Subduction Zone is capable of producing
destructive local earthquakes and tsunamis, and is a major
threat to the west coast of North America (Bernard, 2005).
Most of the energy of the 1992 Cape Mendocino tsunami was
concentrated in coastally trapped edge waves (González et al.,
1995); i.e., in waves that (1) have maximum amplitude at the
coast and rapidly decay seaward; (2) conserve tsunami energy and transfer it along the coast at long distances with very
little energy loss (with the shelf playing the role of a waveguide); and (3) propagate much more slowly than open-ocean
tsunami waves, so they can arrive at specific locations hours
later than expected.
The Pacific-wide tsunami warning that was issued after a
major Shikotan earthquake in the Southern Kuril Islands on 4
October 1994 (roughly 2.5 years after the Cape Mendocino
tsunami) caused confusion among emergency managers,
erratic response of coastal communities and costly evacuations. The 1994 tsunami emphasized the need to reduce false
alarms and improve communication and coordination
between the warning centres and local authorities (Bernard,
2005). The California earthquake of 15 June 2005 occurred in
almost the same area as the 1992 Cape Mendocino earthquake
and generated a detectable tsunami that was similar to the
1992 tsunami, but of smaller amplitude. Although the 2005
tsunami was too minor to create any noticeable damage to
coastal areas, other recent catastrophic tsunami events have
demonstrated that earthquakes, even as small as Mw = 7.1, can
generate locally destructive tsunamis, especially when these
earthquakes are accompanied by submarine landslides. Thus,
the Mw = 7.0 earthquake in Papua New Guinea (PNG) of 17
July 1998 triggered a local landslide and produced 15-m
waves that killed more than 2200 people (González, 1999).
The tsunami warning of 15 June 2005 was a natural response
to the 1998 PNG event and to the catastrophic 2004 Sumatra
tsunami in the Indian Ocean (Lay et al., 2005; Titov et al.,
2005a) where tens of thousands of human lives could have
been saved if the Tsunami Warning System had existed in the
Indian Ocean and timely warning had been declared.
The improved response and preparedness to the 2005
California tsunami compared to the 1992 Cape Mendocino
and the 1994 Shikotan tsunami demonstrates that significant
progress has been achieved.
(1) The 1992 Cape Mendocino tsunami was recorded by
NOAA analogue tide gauges. The only tide gauge with
digital recording (6-min sampling) was at Arena Cove
(California). It is unclear if this tsunami was observed
on the coast of British Columbia because the quality of
the CHS analogue records was not high enough to
detect weak tsunamis. In contrast, the 2005 California
tsunami was clearly recorded by the six digital tide
gauges with 1-min sampling that were positioned along
the US and Canadian coasts. Despite significant background noise, the tsunami was definitely identified in
the records. The signals from these instruments were
rapidly transmitted to the tsunami warning centres.
(2) During the 1992 and 1994 tsunamis, there were no
open-ocean bottom-pressure recorders that could be
used for tsunami warning. The 2005 California tsunami was effectively recorded by two deep-ocean DART
buoys installed off the west coast of the United States.
The precise bottom pressure sensors provided real-time
assessment and detection of 0.4–1.5 cm tsunami waves
at these sites located quite close to the 2005 earthquake
source area. Moreover, within approximately 2.5 min
of the main shock, both instruments recorded seismic
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surface Rayleigh waves and these strong ground oscillations initiated an automatic alarm regime, with data
records transmitted to the tsunami warning centres every
15 seconds. The data from the DART buoys were used
operationally to verify the PMEL/NOAA numerical
model results. Small observed and predicted waves
were the reasons the tsunami warning was cancelled.
(3) Until recently, there have been no effective numerical
models to simulate real-time tsunamis: such models
now exist (Whitmore, 2003; Titov et al., 2005b;
Kowalik et al., 2005). The 2005 California tsunami
was “operationally” numerically simulated; the results
of this simulation were used to predict tsunami wave
heights at coastal locations.
In summary, the small 2005 California tsunami was important from both a scientific and practical point of view. It was
accurately recorded by both coastal tide gauges and openocean bottom pressure sensors, and it was simulated in realtime with model results that matched well with the recorded
DART data. What was especially reassuring is that the coastal
observations, open-ocean DART records and model results
can be used effectively for early tsunami warning cancella-
tion. While the tsunami warning for the 1994 Shikotan tsunami
was not cancelled until after 8 hr 32 min had passed, the 2005
California tsunami warning was cancelled after only 1 hr 18 min.
Acknowledgements
We gratefully acknowledge Vasily Titov, Pacific Marine
Environmental Laboratory (PMEL) NOAA, Seattle,
Washington, who provided us with results from his numerical
modelling of the 2005 California tsunami and Isaac Fine,
Heat and Mass Transfer Institute, Minsk, Belarus, who helped
with the tsunami travel time computations. We also thank Hal
Mofjeld of PMEL/NOAA (Seattle) and Paul Whitmore, West
Coast and Alaska Tsunami Warning Center (Palmer, Alaska),
for assisting with the NOAA tide gauge and DART data, and
Denny Sinnott and Neil Sutherland of the Canadian
Hydrographic Service (Sidney, British Columbia) for helping
us assemble and verify the CHS tide gauge data. We also
thank Maxim Krassovky, University of Victoria, for assisting
with the map plots, Patricia Kimber (Sidney, BC) for drafting
the figures and the two reviewers for their constructive and
valuable comments. Partial financial support was provided by
the Russian Federation through RFBR Grant 05-05-64585.
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ATMOSPHERE-OCEAN 44 (4) 2006, 415–427
Canadian Meteorological and Oceanographic Society