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1. Applications of Satellite Altimeter Data To Tsunami Research
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SSH measurements were used by a number of authors to study the properties of the
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Sumatra-Andaman tsunami, its propagation and scattering from the coastline as well as to
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improve characterization of the seismic source of the tsunami and to verify numerical
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tsunami models (e.g. Smith et al., 2005; Song et al., 2005; Ablain et al., 2006; Hirata et
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al., 2006; Geist et al., 2007; Gower, 2007; Hayashi, 2008; Hoechner et al., 2008).
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2. Method of Splitting Tsunami (MOST) Model
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The two-dimensional SSH fields predicted by the MOST model (Titov and
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Gonzalez, 1997) is based on results from a pre-computed tsunami propagation database
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(Gica et al, 2008). NOAA Center for Tsunami Research (NCTR) has developed a pre-
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computed tsunami propagation database, which consists of 1,718 pre-computed model
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runs, covering along all known faults zones in the Pacific and Atlantic Basins and the
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Indian Ocean. For further details on the computation of the events in the tsunami
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propagation database and MOST model output, the reader should consult the references
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(Gica et al., 2008; Hamlington et al., 2011).
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The initial sea surface displacement resulting from this procedure is refined once
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the actual tsunami signals are detected by the Deep-Ocean Assessment and Reporting of
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Tsunamis (DART) buoys. The first DART detected the tsunami wave peak for the 2011
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Tohoku tsunami at around 0.55 hours after the earthquake with a second DART detecting
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the tsunami at 1.12 hours after the earthquake. Placement of the DART buoys has been
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selected to avoid seismic signals contaminating the tsunami signal that is being detected.
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The proximity of the earthquake to the near-field coastlines of Japan did not provide
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enough lead-time for a faster response, and a near-field forecast from the DART buoys
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(or any other measurement system) was a challenge since the tsunami arrived at the
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closest coastline before the DART buoys detected the tsunami waves.
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3. Statistical Randomization Tests of Sea Surface Roughness
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One thousand 3.2-windows were randomly selected from the area of the ocean
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through which the tsunami passed. Mean 0 values were subtracted in each window to
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calculate the 0 anomaly, and the RMS values and the number of zero crossings were
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calculated for the 0 anomaly in each window. These values were compared to the
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respective values in the 3.2-window containing the leading edge of the tsunami. The
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RMS 0 anomaly characterizes the strength of the surface roughness variations, while the
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number of zero crossings gives a measure of the spatial scale of these variations. If the
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tsunami-induced variations were distinctive and unique, we would expect the window
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containing the leading edge of the tsunami to have both a higher RMS and a greater
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number of zero crossings than found in the 1000 randomly selected windows (Godin et
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al., 2009; Hamlington et al., 2011). Since the satellite altimeters sampled both the leading
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edge of the tsunami and the tsunami wave field beyond the leading edge, we use a
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“sliding window” approach to test every 3.2 segment of a tsunami-affected altimeter
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pass. For further details of the theoretical underpinning regarding the tsunami-induced
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roughness variations and the statistical randomization tests, the reader is referred to
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Godin et al. (2005; 2009) and Hamlington et al. (2011).
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Randomization tests are performed to determine if roughness variations caused by
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the passage of the tsunami were significantly different from variations found in the region
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at times other than during the tsunami. Selecting 3.2° windows centered across Envisat
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pass 419 of cycle 100, however, we see that the variations in the sea surface roughness on
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the day of the tsunami were not significantly different from the variations present at other
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times (Fig. S1A). Using the theory discussed in Godin et al. (2004; 2009), the expected
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σ0 anomaly RMS values can be predicted for pass 419 of cycle 100. With wind speeds
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between 7 m/s and 13 m/s in the region as measured by the Special Sensor
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Microwave/Imager (SSM/I) instrument on the day of the tsunami, and a tsunami wave
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amplitude of around 20 cm, σ0 anomaly RMS values are theoretically predicted to be near
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0.10 dB, which is in good agreement with the observed RMS value of 0.16 dB for the
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3.2° window containing the leading edge. This small RMS value is the likely cause of the
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inability to detect the tsunami-induced variations in sea surface height using the
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randomization test. Applying the same randomization tests to Jason-1, however, shows
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that there is less than 1% chance that the observed sea surface roughness variations on the
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day of the tsunami in the region between 5°N and 10°N would occur at any other time.
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Again the theory can be used to predict the RMS value of the tsunami-induced variations.
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With wind speeds between 4 m/s and 10 m/s, and tsunami wave amplitude between 40
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cm and 50 cm, the predicted RMS value is found to be between 0.25 dB and 0.70 dB.
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This agrees with the measured RMS value of 0.55 dB from the window in Jason-1 pass
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147 of cycle 338 containing the leading edge of the tsunami. As a result of the larger
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amplitude and lower wind speeds, the RMS variations induced by the tsunami are much
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more pronounced, leading to the positive identification from the randomization tests on
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the sea surface roughness measurements.
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4. Statistical Analysis of Jason-2
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The SSH data from Jason-2 pass 21 of cycle 99 is filtered by removing the
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smoothed SSH data from pass 21 of the previous cycles, as described in section 2. By
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sampling the results produced by the MOST model along this pass, we can compare the
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filtered SSH data to the model output. Fig. S1A shows the filtered SSH data with the
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MOST model results overlaid. Jason-2 enters the tsunami wave field near the equator
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with the leading edge found near 10°S. The comparison with the MOST model shows an
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apparent time discrepancy between the observations and model results. It is found that the
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best fit of the MOST model to the observations occurs with a small delay of only 2
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minutes. The amplitude of the tsunami from the MOST model estimate, however, appears
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to be less than what is found from the filtered satellite altimetry. Using the test described
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in section 3 that was applied to Envisat and Jason-1, it is possible to determine if the
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correlation and amplitude agreement between the observations and model data for pass
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21 are exceptional. The computations were again done for the MOST model with time
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lags of +/-15 minutes, leading to 31 data points for each cycle. Fig. S1B shows the results
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using the data in the window between 15°S and the equator with a peak correlation of
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0.65, lag time of 2 minutes and an RMS ratio of 1.84.
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The same “sliding window” test on the sea surface roughness variations used in
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section 3 was applied to the Jason-2 measurements on pass 21 of cycle 99. The SSH
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signal in pass 21 was not large, showing amplitudes of less than 10 cm in the MOST
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model, so positive identification in the sea surface roughness measurements is not
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expected. As seen in Fig. S1C, however, the probability of seeing similar σ0 variations to
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those observed on the day of tsunami around 10°S is around 10%. This suggests that the
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tsunami signal amplitude is underestimated in the MOST model and closer in reality to
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the 40 cm peak-to-trough amplitude observed in the filtered satellite altimetry SSH
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measurements.
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5. Expected Satellite Altimeter Response Times
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To determine how quickly one should expect an altimeter to overfly a tsunami
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occurring at the Tohoku location, a randomization test was performed in which altimetry
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data was collected from Jason-1 and Envisat 15 days before and after the day the Tohoku
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tsunami occurred. One hundred dates and times were picked at random within these 30
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days and these times were set to be the onset of the tsunami. Using the MOST model, the
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time of the first altimeter pass that would have been coincident with the tsunami wave
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field was determined. One hundred trials were conducted using only Jason-1, only
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Envisat, and finally using both Envisat and Jason-1. The mean times of the first satellite
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altimeter over-flight determined from the tests were 4.7 hours for Jason-1, 4.2 hours for
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Envisat, and 3.4 hours for both altimeters combined. Based on this, with both Envisat and
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Jason-1 available, one would expect an altimeter to sample the tsunami wave field 3.4
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hours, on average, after the generation of the tsunami. This suggests that the altimeter
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sampling times for the actual Tohoku tsunami were worse than should have been
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expected.
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Since the Tohoku tsunami, the availability of satellite altimetry measurements has
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changed. Envisat is no longer functioning and Jason-1 has been moved to a new orbit.
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Despite these developments, the analysis regarding expected response times is still
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relevant. Given the similarity of the respective repeat orbits, Jason-2 has a response time
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close to that of Jason-1 as given above. New altimeters will be launched in the coming
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years (including the Surface Water Ocean Topography mission in the next decade), and
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will supplement the measurements provided by satellite altimeters already in operation.
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The potential response time of a satellite altimeter is highly dependent on the orbit, and it
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is not possible to make general statements about response time from satellite altimeters.
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Nevertheless, the numbers given above provide insight into what can be expected with
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the response time from satellite altimeters in the future.
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References
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Ablain, M., Dorandeu, J., Le Traon, P.-Y., and Sladen A. (2006), High resolution
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altimetry reveals new characteristics of the December 2004 Indian Ocean
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tsunami, Geophys. Res. Lett., 33, L21602, doi:10.1029/2006GL027533.
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Gica, E., Spillane, M.C., Titov, V.V., Chamberlin, C.D. and Newman, J.C. (2008),
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Development of the Forecast Propagation Database for NOAA’s Short-Term
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Inundation Forecast for Tsunamis (SIFT), NOAA Technical Memorandum OAR
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PMEL-139.
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Hayashi, Y. (2008), Extracting the 2004 Indian Ocean tsunami signals from sea surface
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height data observed by satellite altimetry, J. Geophys. Res., 113, C01001,
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doi:10.1029/2007JC004177.
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Hirata, K., Satake, K., Tanioka, Y., Kuragano, T., Hasegawa, Y., Hayashi, Y., and
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Hamada, N. (2006), The 2004 Indian Ocean tsunami: Tsunami source model from
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satellite altimetry, Earth Planets Space, 58, 195–201.
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Hoechner, A., Babeyko, A. Y., and Sobolev, S. V. (2008), Enhanced GPS inversion
technique applied to the 2004 Sumatra earthquake and tsunami, Geophys. Res.
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Lett., 35, L08310, doi:10.1029/2007GL033133.
Smith, W. H. F., Scharroo, R., Titov, V. V., Arcas, D., and Arbic, B. K. (2005), Satellite
altimeters measure tsunami, Oceanography, 18, 11–13.
Song, T. Y., Ji, C., Fu, L.-L., Zlotnicki, V., Shum, C. K., Yi, Y., and Hjorleifsdottir, V.
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(2005), The 26 December 2004 tsunami source estimated from satellite radar
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altimetry and seismic waves, Geophys. Res. Lett., 32, L20601,
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doi:10.1029/2005GL023683.
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Titov, V.V. and Gonzalez, F.I. (1997), Implementation and Testing of the Method of
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Splitting Tsunami (MOST) Model, NOAA Technical Memorandum ERL PMEL-
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112.
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Figure S1. Results of statistical randomization tests on σ0 anomaly values using a “sliding
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window” for (A) Envisat pass 419 of cycle 100, (B) Jason-1 pass 147 of cycle 338. A
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randomization test is conducted for every 3.2° window and the statistical significance is
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computed to test the hypothesis that the surface roughness variations with and without the
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tsunami present are not significantly different. Low probabilities indicate that the values
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computed during the tsunami were exceptional. The x-axis values represent the center
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point of the window.
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Fig. S2. (A) Comparison of filtered SSH data (red) with the MOST (blue dashed) model
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results for Jason-2 pass 21 of cycle 99. (B) Correlation between MOST model and
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filtered SSH data and ratio of RMS values of SSH data and MOST model are shown for
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observations during the Tohoku tsunami (squares) and historical observations (circles) for
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Jason-2 pass 21. (C) Results of statistical randomization tests on σ0 anomaly values using
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a “sliding window” for Jason-2 pass 21 of cycle 99.