Tide−Tsunami Interaction in Columbia River, as Implied by Historical Data and Numerical Simulations
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- Tolkova, E. Pure Appl. Geophys. (2013) 170: 1115. doi:10.1007/s00024-012-0518-0
The East Japan tsunami of 11 March 2011 propagated more than 100 km upstream in the Columbia River. Visual analysis of its records along the river suggests that the tsunami propagation was strongly affected by tidal conditions. A numerical model of the lower Columbia River populated with tides and a downstream current was developed. Simulations of the East Japan tsunami propagating up the tidal river reproduced the observed features of tsunami waveform transformation, which did not emerge in simulations of the same wave propagating in a quiescent-state river. This allows us to clearly attribute those features to nonlinear interaction with the tidal river environment. The simulation also points to possible amplification of a tsunami wave crest propagating right after the high tide, previously deduced from the recordings of the 1964 Alaska tsunami in the river.
KeywordsTidetsunaminonlinear interactionnumerical modelingColumbia River
Tides and tsunamis are both long waves whose simultaneous propagation is governed by the shallow-water equations (SWE). In deep water, they should not affect each other. In shallow regions with dominating tidal signals, a tidal wave might have an effect on tsunami propagation through the nonlinear terms in SWE.
It has been demonstrated in numerical simulations that sea surface elevation, currents, and extent of inundation computed when tide and tsunami waves were simulated together might differ significantly from the mere sum of the corresponding values obtained when simulating the tide and the tsunami separately (Kowalik et al., 2006; Kowalik and Proshutinsky, 2010). The deviation from the linear superposition was found to depend on the tidal phase. Kowalik and Proshutinsky (2010) numerically investigated tsunami coupled with tides propagation into Cook Inlet, Alaska. Cook Inlet is a narrow bay, 250 km in length to the north of Kodiak Island. It lies on the Alaskan continental shelf where tides are very strong. The bay is approximately 100 m deep at the entrance, but becomes as shallow as 25 m deep by its middle region. Their conclusion was that a 100 cm high tsunami wave near the entrance would become 395–605 cm high at Anchor Point (about 1/5 of the length of the Inlet) and 5–135 cm high at Anchorage at the end of the inlet, depending on the tidal phase. In Anchorage, the highest tsunami amplitude of 135 cm is expected on transition from low to high tide, with nearly the same expected on transition from high to low, while the lowest tsunami wave of 5 cm is expected with the high tide (Kowalik and Proshutinsky, 2010).
While the interaction appears to be significant, evidence for it is scarce. Cook Inlet in particular is naturally well protected from tsunamis, except those of local origin, which occurred when the area was not well instrumented. The East Japan tsunami of March 2011 was recorded at the Kodiak tide gauge with an amplitude of 25 cm, but was undetectable on gauge records in Cook Inlet. Hence there is no historical evidence to confirm the above patterns of tsunami interaction with tides.
One type of environment where one might look for signatures of tide–tsunami interaction is a tidal river, where tsunamis can propagate far upstream on top of the tides. Since both waves (tide and tsunami) travel at the same speed, each tsunami wave crest is locked with the specific tidal phase, whereas the tsunami activity might persist for hours and days, thus allowing observation of the interaction with tides at different tidal phases. Observations can only be made in well-instrumented rivers, and significant upstream penetration could only occur during a major tsunami event.
The physics of tsunami propagation up the river, particularly in interaction with tides, was discussed at the Workshop on Tsunami Hydrodynamics in a Large River held at Oregon State University in Corvallis, Oregon, 15–16 August 2011 (http://www.isec.nacse.org/workshop/2011_orst/agenda.html).
Below, evidence of tide–tsunami interaction in existing records of tsunamis entering the Columbia River is discussed, with an emphasis on the East Japan tsunami of 11 March 2011. We proceed by numerically recreating a realistic environment of the Columbia River on the day of the tsunami. Once the tidal river model had been developed, a numerical simulation of the East Japan tsunami propagation up the river was performed, with a de-tided record of a nearby DART® station (deep-ocean tsunami detector) used to supply the tsunami input into the model. To isolate tidal river influence on the tsunami propagation, two cases were considered: propagation into the still basin (quiescent-state river: no tides, no river flow) and propagation up the river populated with tides and downstream current (tidal river). The purpose of the simulations is to attribute the observed features of tsunami waveform transformation to nonlinear interaction with the tidal river environment.
2 Tsunami Recordings in the Columbia River
There are records of tsunamis propagating up the Columbia River, the largest river on the west coast of North America.
Distances and propagation times from the river’s mouth to the locations
Tsunamis are also known to penetrate great distances up the Columbia River. Lander and co-authors (1993) presented a collection of marigrams recorded at Astoria (27 rkm), that display signals of four tsunami events on 23 August 1872, 4 November 1952, 23 May 1960, and 28 March 1964.
The 1964 Great Alaskan tsunami was recorded at five tide gauge stations along the river. Marigrams show approximately 0.6 m crest-to-trough variations from the tidal level at Astoria, 0.3 m at Beaver (86 rkm mark), and a small but measurable tsunami signal at Vancouver, Washington, 170 rkm from the ocean (Wilson and Torum, 1972a). Those marigrams can also be found in Talke (2011).
All the event records at Astoria display the same pattern: tsunami amplitude is noticeably smaller on receding tide compared to its value on rising tide. Wilson and Torum observed that the tsunami signal in the Beaver and Vancouver records of the 1964 Alaska tsunami can only be detected atop high tide: ”Beaver tide gage, in particular, shows that, with the exception of the tsunami waves riding the tide crest, the intermediate waves have lost their identity and hardly register at low tide, though later waves are found again on the succeeding high tide” (Wilson and Torum, 1972b).
Tsunami wave envelopes in the estuary (Astoria) and at its exit (Skamokawa) are significantly different.
The tsunami arrives at Astoria at about the 16 h mark, at receding tide. During the first 4 h (until the tide starts to rise) the record at Astoria displays noticeably smaller tsunami amplitude than in the next few hours. Contrary to this, the tsunami record at DART station 46404 located 230 nmi west of Astoria (Fig. 4) suggests that the tsunami had larger amplitudes in the first 4 h.
At Skamokawa, the tsunami is not evident before the 22 h mark, at the beginning of the rising tide. Since the long-wave travel time between the two locations is 56 min (see Table 1), the initial 4–5 h long tsunami wave train riding the receding tide appears to attenuate within the estuary and never penetrate into the upper river. The signal level also falls quite suddenly on the next major falling tide (at the 40 h mark at Longview).
In addition to the amplitude modulation imposed by the tide, the record at Skamokawa does not display shorter wave periods, which are present in the Astoria record. Shorter waves experience more scattering in the estuary and do not penetrate into the channel.
The records in the channel show essentially the same signal. There were no changes, except for a gradual reduction in amplitude, which occurred as the tsunami propagated past Skamokawa.
There might be evidence of another interaction effect. Wilson and Torum (1972b, pp. 482–484), in their analysis of the 1964 Alaska tsunami penetration up the river, deduced amplification of the wave immediately following the tidal crest. They reconstructed tsunami crest elevations above the tidal level of the first five tsunami waves, as they traveled along the river, from the mouth to Vancouver, Washington. The first wave entered the river 1.5 h ahead of high tide. The second wave entered just after high tide (1.8 h after the first wave). According to the reconstruction, the second wave grew in height as it traveled to Skamokawa. However, this can not be confirmed, given that from the mouth to Beaver (31 rkm upstream Skamokawa), the tsunami was recorded at only one location, at Astoria. The reconstruction itself is based on a rather limited amount of data and can not be considered accurate. Wilson and Torum explained the suspected amplification by the presence of a tidally induced standing wave with 60 nmi wavelength and 3.6 h period, with an antinode located at 33 nmi (61 rkm). When the second tsunami wave passed a positive antinode, the oscillations added up to the observed wave height. The first and the third tsunami waves were 1.8 h, or half the standing wave period, apart from the second, and therefore passed the antinode when it was negative. This explanation attributes the effect to a linear superposition of tidal and tsunami motion, rather than to nonlinear interaction of the two waves, which is of interest here.
Below, tsunami propagation in a river populated with tides and downstream current is simulated numerically, with the objective of reproducing the observations and deducing on their nature.
3 Simulation of Tidal River
An attempt was made to imitate a realistic environment of the Columbia River. At the river’s mouth, the numerical tide was composed of M2 and K1 tidal constituents. As the tide propagates upriver, it interacts with the river current, dissipates, over-tides are generated, and the tide transforms. Tidal propagation in channels is mostly affected by interaction with bathymetric/topographic features and by friction, whose effect is greatly increased by river flow, if present (Jay, 1991). Our simulation accounts for those factors, though in a depth-averaged approximation, by using detailed bathymetry of the Columbia River basin and by combining tidal motion with downstream flow, subject to bottom friction. The numerical solution sought should be able to approximate tidal records from gauges along the river in tidal range, shape, and vertical datum.
Simulations were done using the Method Of Splitting Tsunamis (MOST) numerical model (Titov and Synolakis, 1998; Burwellet al., 2007), adopted by National Oceanic and Atmospheric Administration (NOAA) for tsunami forecasting operations (Tanget al., 2009). Frictional acceleration f due to bottom friction in a wide channel, experienced by a particle in a water column of height h moving with velocity V, was given by the Manning formula (Stoker, 1957) f = n2g|V|V /h4/3, with n = 0.03 sec/m−1/3, and g being gravity acceleration. A river discharge was set to 8,200 m3/sec. Our simulation domain for the lower Columbia River enclosed an 85 rkm long segment, from the mouth on the west boundary to Beaver on the east. The computational grid has 20 m spacing with 3,425 nodes in the west-east (x) direction and 1,001 nodes in the south–north (y) direction.
Conventionally, a tsunami model computes tsunami propagation in a still basin (ocean) with possible run-up on shore, given initial and boundary conditions. Simulating realistic tidal motion in a segment of a river with a tsunami model is a challenging task, in that every component of the required model input is unknown, namely, the initial distribution of surface elevation and currents, consistent with given downstream flow and tidal phases in the river segment, as well as time histories of elevation and currents across the river at downstream and upstream ends of the segment.
The first step toward solving the problem was to part downstream and upstream boundary conditions. This was achieved by appending the river segment with a straight west-to-east channel 200 nodes long, with spacing gradually increasing from 20 m on the west (as in the rest of the river) to 4,000 m on the east. Consequently, the length of the river segment in the simulation increased from 85 rkm to L = 745 rkm, being enclosed within a 3,645 × 1,001 node grid. The main purpose of this extension was to move the upstream boundary farther away from the river’s mouth, where no tide or tsunami would reach. Thus the upstream boundary conditions become independent of variations of the ocean-side input and are determined only by the downstream current.
The channel also simplifies importing waves into the model by serving as a ”depth adaptor”. The depth profile across the channel transitions smoothly from the river depth profile d(y) on the side connected to the river to a flat profile of an average depth <d> = 16 m at the opposite end. Thus the upstream boundary elevation and west-to-east velocity component can be assumed constant across the channel, with the other velocity component being zero.
It should be noted that MOST solves the SWE and formulates boundary conditions in terms of Riemann invariants. Boundary conditions are used to compute an in-going Riemann invariant rather than prescribe velocities and elevation at the boundary nodes. Thus, as long as velocities and elevation being imported through the boundary do not represent the true solution, they do not coincide with the model solution on the boundaries.
However, while the upstream input (2) coincides with the model solution on the corresponding boundary, the downstream input (3) does not, due to the ocean-side adaptor being too short to avoid some reflection back from the river mouth. Thus coefficients α, β, and time lag τ in (4) were found in simulations aimed on approaching the tidal record in Astoria. Likewise, (5) provides only an estimate for γfl, which needs to be adjusted in the simulations to provide the desired average flux through the river’s mouth. After a number of trials, the following values were obtained: α = 1.20, β = 0.96, τ = 133 min, and γfl = 0.2 m/s, which is 30 % above its estimate according to (5).
Since the initial conditions do not contain tidal motion, it takes at least 15 h of simulation time for the solution to develop, so the simulation is started 25 h prior to the tsunami arrival. After the solution with the upstream input (2) and downstream input (3) was computed for 70 h of simulation time, the resulting time histories on the boundary with the ocean were used as the true downstream input of the tidal river model. Corresponding initial conditions were extracted from the same solution. In subsequent simulations of the tsunami propagation up the tidal river, tsunami input was combined with the true downstream input of the tidal river model.
4 Simulation of the 2011 East Japan Tsunami Propagation up the Columbia River
To isolate tidal river influence on the tsunami propagation, two cases were considered: propagation in the quiescent-state river and propagation up the tidal river. In this work, tidal motion in a river is always considered coupled to the river flow, while a quiescent-state river contains no river flow. Hereafter, motion comprised of ocean tide and downstream current is referred to as the river tide. Tsunami input was added to the downstream input of the tidal river model developed above, to numerically simulate the propagation of the East Japan tsunami coupled to the river tide.
During the first 4–5 h, tsunami activity at Astoria is noticeably lower than on the next rising tide. This is not the case in the quiescent-state river, where, in essence, the wave envelope in Astoria follows that of the incoming wave, and the initial waves are high. The signal level falls again 24 h later, on the next major falling tide.
The tsunami at Skamokawa is barely visible before the tide starts to rise (near the 23 h mark). That is, the first 5 h long wave train arriving with the receding tide dissipated in the estuary almost completely. This is not the case in the quiescent-state river, where the initial waves are clearly present and as high, relative to the later waves, as they were in the ocean.
In both cases, simulated records at Skamokawa do not contain the higher frequencies observed within the estuary (at its entrance and in Astoria).
The tsunami wave envelope through the fluvial channel (as shown at Beaver) resembles what is found at Skamokawa.
The simulation of tsunami propagation in the tidal river has reproduced the observed features of tsunami waveform transformation, that cannot be replicated in the simulation of the same wave propagating in a quiescent-state river. Tsunami attenuation as tide transitions from high to low therefore shows tsunami interaction with river tides due to mechanisms accounted for by the shallow-water approximation. Upstream of the estuary, the tsunami wave has larger amplitude when it rides the high tide, as noticed in the records of the 1964 Alaska tsunami.
The simulation also points to amplification of a tsunami wave following the higher high tide between Astoria and Skamokawa, relative to a wave propagating in the still basin. In Fig. 9, heights of tsunami waves in the tidal river and in the quiescent-state river are equal at the Astoria, 37-h mark. Upon arrival at Skamokawa at the 38-h mark, the wave in the tidal river is twice as high as it is in the still basin (though still not higher than it was at Astoria). It is possible, that some amplification of a tsunami wave following the high tide on its way to Skamokawa in 1964, suspected by Wilson and Torum (1972b), and the similar behavior emerged in the simulation have the same cause. Based on the simulations, the cause should be attributed to nonlinear interaction with the river tide, since any background signal in the basin, whether propagating or standing wave, would be eliminated by de-tiding as long as it was superimposed on the tsunami in a linear fashion.
The East Japan tsunami of 11 March 2011 penetrated worldwide and provided an unprecedented level of observations. Records from this event allow us to look for phenomena which could not be clearly detected before.
In this work, the records of the 2011 East Japan tsunami in the Columbia River are analyzed for signatures of tide–tsunami interaction. Two major signatures of tidal river influence have been observed. In the lower estuary, interaction with river tides appears to favor tsunami propagation on rising tide. In the upper estuary and further upstream, the interaction favors tsunami propagation at the very top of the tide. A numerical model of the lower Columbia River populated with realistic tidal motion coupled to a river flow was developed. Simulations of the East Japan tsunami propagating up the tidal river reproduced the observed features of tsunami waveform transformation, which were not replicated in simulations of the same wave propagating in a quiescent-state river. This allows us to attribute, with certainty, those features to nonlinear interaction with river tides. The simulation also points to possible amplification of a tsunami wave crest propagating right after the high tide, as previously suspected from the recordings of the 1964 Alaska tsunami in this river.
Tide–tsunami interaction manifested itself differently in simulations by Kowalik and co-authors (2006, 2010) of tsunami propagation onto a hypothetical 1-D continental shelf and into Cook Inlet, as mentioned in the introduction. However, Kowalik and co-authors simulated interaction with a standing (as opposed to propagating) tidal wave (phase angle of 1.5 π between elevation and velocity time histories in a simulated tidal wave (Kowalik and Proshutinsky, 2010)). A standing wave seems to dominate the tidal motion in Cook Inlet as well. Thus the tsunami interacts with different tidal phases as it travels over the tide, as opposed to the case when a tsunami rides the tide and each tsunami wave crest is locked with the specific tidal phase. The results of all the simulations suggest that interaction signatures depend on the environment in which the interaction occurs.
This work was supported by the Joint Institute for the Study of the Atmosphere and Ocean (JISAO, University of Washington) under NOAA Cooperative Agreement No. NA10OAR4320148, Contribution #1889 (JISAO), #3775 (Pacific Marine Environmental Laboratory, NOAA). The study was originally motivated by the Workshop on Tsunami Hydrodynamics in a Large River held at Oregon State University, Corvallis, OR, 15–16 August 2011 (http://www.isec.nacse.org/workshop/2011_orst/agenda.html). Columbia River bathymetry was provided by Dr. Joseph Zhang (Oregon Health and Science University) and Prof. Harry Yeh (Oregon State University) as part of the workshop materials. Beaver tide gauge record is courtesy of the U.S. Geological Survey, Oregon Water Science Center (http://www.or.water.usgs.gov/). Gauge records at other Columbia River locations used in this work have been obtained from the NOAA/NOS/CO-OPS public website (http://www.tidesandcurrents.noaa.gov/). DART record was obtained from NOAA’s National Data Buoy Center public website (http://www.ndbc.noaa.gov/dart.shtml). Sincere thanks to Sandra Bigley (PMEL), Jean Newman (PMEL), and Stewart Allen (Centre for Australian Weather and Climate Research) for language-editing the manuscript.