Ocean Engineering 38 (2011) 1677-1685
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O C E A N
Ocean Engineering
E L S E V I E R j o u r n a l homepage: w w w . e l s e v l e r . c o m / l o c a t e / o c e a n e n g
Automatic, real-time detection and characterization of tsunamis in deep-sea
level measurements
Gian Mario Beltrami
Dipartimemo di Ingegneria delle Strutwre, delle Acque e del Terreno (DISAT). Laboratorio di Idraulica Ambientale e tvlarittima (LIAIvI), Université degli Studi di L'Aqiiila, Monteluco di Roio, 67040 L'Aquila, Italy
A R T I C L E I N F O A B S T R A C T
Article history:
Received 21 October 2010 Accepted 3 0 j u l y 2011 Editor-in-Chief: A.I. Incecik Available online 19 August 2011
Keywords:
Tsunami detection Tsunami characterization Algorithm
Real-time
Tsunami early warning systems
T h e a l r e a d y e x i s t i n g a l g o r i t h m s for a u t o m a t i c , r e a l t i m e t s u n a m i d e t e c t i o n i n d e e p s e a level m e a s u r e -m e n t s , a l t h o u g h c a p a b l e of d e t e c t i n g a t s u n a -m i , fail in c h a r a c t e r i z i n g it in t e r -m s of b o t h a -m p l i t u d e a n d p e r i o d . S u c h a c h a r a c t e r i z a t i o n is c a r r i e d o u t by p o s t p r o c e s s i n g the o b s e r v a t i o n s once a v a i l a b l e . A delay b e t w e e n t s u n a m i d e t e c t i o n a n d c h a r a c t e r i z a t i o n s h o u l d be therefore a c c e p t e d . T h e p r e s e n t n o t e suggests a s i m p l e m o d i f i c a t i o n of t h e e x i s t i n g a l g o r i t h m s capable of g u a r a n t e e i n g t h e c o n t e m p o r a -n e o u s d e t e c t i o -n a -n d c h a r a c t e r i z a t i o -n o f a t s u -n a m i , a u t o m a t i c a l l y a -n d i-n r e a l - t i m e . T e s t s c a r r i e d out u s i n g a c t u a l l y m e a s u r e d t i m e s e r i e s s h o w the e f f e c t i v e n e s s of the p r e s e n t e d m o d i f i c a t i o n . © 2011 E l s e v i e r L t d . A l l rights r e s e r v e d . 1. Introduction
At present, two algorithms expressly designed to detect a tsunami i n real-time w i t h i n deep-sea level measurements have been already published: the DART algorithm developed by Mofjeld (1997) under the NOAA's Deep-ocean Assessment and Reporting of Tsunamis program (Gonzalez et al., 1998; Milburn et al., 1996); and the ANN algorithm (Ardficial Neural Network) proposed by Beltrami (2008). Currently, two further algorithms are being developed (Pignagnoli et al., 2010; Bressan and Tinti, 2010). These last algorithms have been presented at the EGU General Assembly 2010, but have not been published yet.
As i t is known, deep-sea level measurements are usually collected at a standard sampling interval of 15 s by bottom pressure recorders (BPRs) located at water depths ranging f r o m hundreds to some thousands of meters (e.g. Eble and Gonzlez, 1991). It is at such water depths that BPRs can exclusively detect pressure fluctuations induced by propagadng waves w i t h i n the tsunami and tidal frequency band. The main 'disturbances' (non-tsunami waves) recorded by a BPR are therefore the astronomical and the meteorological tide.
The DART and the ANN algorithm use a cubic polynomial and an artificial neural network respectively in order to predict the non-tsunami waves present in the observations. The assumption is that a close prediction of such 'disturbances' makes it possible to filter them out simply by subtracting the values observed f r o m
E-mail addresses: gianmario.beltrami@univaq.lt, beltrami@ing.univaq.it
0029-8018/$-see front matter © 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.oceaneng.2011.07.016
those predicted. The actual propagation of a tsunami can then be monitored by checking the amplitude of the filtered signal against a prescribed threshold. The amplitude of a perfectly filtered signal should, i n fact, be equal to zero i n the absence of a propagating tsunami.
Although both the algorithms can actually detect a tsunami, they can neither properly identify its waveform, nor characterize it i n terms of amplitude and period. This is a consequence of the way i n w h i c h the predictions (and therefore the filtered signal) are calculated. The DART (Mofjeld, 1997) and ANN algorithm (Beltrami, 2008) update the predictions Cp every sampling inter-val (i.e. every 15 s). In the algorithms' standard version, the prediction time is set equal to 15 s i n the future w i t h respect to the actual time. The same p-minute averages ( (centered at the p/2 m i n ) of observations ( collected over the preceding 3 h and p m i n are used by the DART algorithm as polynomial fitting points, and by the ANN one as inputs to a two adaptive-weight feed-forward network. The averaging interval p is generally set equal to 10 m i n (Mofjeld, 1997; Beltrami, 2008), so that the prediction time is set equal to 5 m i n and 15 s in the future w i t h respect to the time at which is centered the first average. It is clear that an actual propagating tsunami influences the predic-tions by affecting the observation averages. As a consequence, the calculated filtered signal does not represent the actual tsunami, although the variation of its amplitude is sufficient to detect an anomaly and therefore to show that a tsunami is actually propagating. In conclusion, the existing algorithms cannot iden-t i f y and characiden-terize iden-the w a v e f o r m of a deiden-teciden-ted iden-tsunami. Such an identification and characterization should be carried out by
1678 C M , Beltrami / Ocean Engineering 38 (2011) 1677-1685 postprocessing the observations, once available. A delay between
tsunami detection and characterization should be therefore accepted.
By the way of example (see:Eble and Stalin, 2007), BPRs i n the currently existing DART network are usually in 'monitoring mode' or 'standard mode' and report data on a six-hour transmission schedule. Six, hourly messages, of four 15-second observations at 15-minute intervals each, are reported in these transmission blocks. The transmission mode is converted to 'rapid reporting mode' or 'event mode' as soon as the filtered signal exceeds the prescribed threshold. Data are then transmitted for a minimum period of 3 h. During this time, 4 m i n of 15-second observation blocks are reported, starting to become available w i t h less than a 3-minute delay (see Meinig et al., 2005). The postprocessing phase, and the full characterization of a tsunami, is therefore delayed of some minutes. When BPRs are located far away from the coasts of interest (as in the case of the DART network), such a delay w i l l not affect the overall efficiency of the system i n providing timely warning of actually approaching tsunamis, and a correct level of tsunami alert. Nevertheless, this is not always the case. When a shorter distance separates a BPR's location f r o m the coast of interest (as would be the case in the Mediterranean Sea), a contemporaneous detection and characterizarion of tsu-namis w i l l be necessary i n order to guarantee a correct level of tsunami alert.
A possible and very simple way to make the DART and ANN algorithm capable of guaranteeing the automatic, real-time detection and characterization of a tsunami is that of lengthening the time interval between the actual and the prediction time. The present note investigates the effects of such a modification, testing i t using actually measured time series. In particular, three different sets of observations (Table 1) were downloaded f r o m the DART program official site (http://nctr.pmel.noaa.gov/Dart/). Two sets were collected during the testing phase of the DART program ('retrospective data') by two BPRs (ak73 and d l 2 5 ) respectively deployed in the Northern (Alaska) and Equatorial Pacific. Both these sets cover a period of observations of around one year and are displayed in PSIA. The third set refers to the observations collected between January 1 and March 3, 2010, by the BPR o f t h e DART station 32412, located 630 nautical miles Southwest of Lima, Peru. In this case, pressure data (although recorded in PSIA) are displayed i n meters of water mH20, and are mainly available w i t h a sampling interval equal to 15 m i n . The data observed on February 27, 2010 (date of occurrence of the most recent Chilean earthquake) constitute an exception, as they are available w i t h a sampling interval equal to 60 and 15 s. A spline was fitted to the available time series i n order to synthesize a series w i t h a constant sampling interval equal to 15 s.
All pressure data—displayed either in PSIA or mH20—were first converted i n Pascals (Pa), and then in meters (i.e. i n sea levels) by dividing them for the mean specific (unit) sea-water weight y = p g at the BPR location, being p the mean sea-water density that should be applied i n order to make the mean sea level resulting from the recorded data equal to the declared BPR water depth. Fig. 1 shows three tracks of the considered observa-tion sets (plotted in terms of sea level variaobserva-tion w i t h respect to
Table 1
Analyzed sets of pressure observations.
Station ID Depth (m) Sampling Location Unit Interval(s)
ak73 4575 15 52.018 N-155.724 W Psia d l 2 5 4500 15 8.487 S-125.018 W Psia 32412 4325 900, 60, 15 17.975 S-86.392 W mHzO
the mean sea level). It is to be noticed that the event that took place on February 27, 2010 following the Chilean earthquake is evident in the lower graph.
The note is structured as follows. The detection performance of the DART and the ANN algorithm is illustrated in the next section, showing that both the algorithms fail in characterizing a tsunami waveform. The procedure to modify the DART and ANN algorithm is illustrated i n Section 3, while the effects of such a modification are given in Section 4. Finally, observations are made and conclusions drawn in Section 5.
2. DART and ANN algorithm detection performance
As already stated, although both the DART and the ANN algorithm can actually detect a tsunami, they can neither properly identify its waveform, nor characterize i t i n terms of amplitude and period. In order to show this, the data recorded on February 27, 2010 by the BPR of DART station 32412 were analyzed. A 8.8 Mw-magnitude earthquake occurred off the coast of the Chilean Maule Region on that date. Following the earthquake, a tsunami was generated, propagating towards the Chilean coasts and radiating in the Pacific.
The data recorded between 06:30 and 11:30 UTC on February 27, 2010 are shown i n the upper graph of Fig. 2 by a black continuous line. At 06:40 UTC, Rayleigh waves are evident in the recorded signal. The propagating tsunami arrived at the BPR location around 09:40 UTC, reaching its maximum amplitude (around 0.24 m over mean sea level) around 09:50 UTC. In the graph, the black dashed line refers to the tidal wave. These data were obtained by filtering out the components w i t h period shorter than 8 h f r o m the original record. The grey continuous line represents the ANN algorithm prediction, being the predic-tion time set equal to 5.25 m i n i n the future w i t h respect to the time at which is centered the first average. As it can be noticed, after few minutes, the ANN predictions tend to follow the observations. This is due to the fact that the tsunami has started to influence the first of thé observation averages that represent the inputs to the network. It is to be noticed that the network adaptive weights resulted f r o m a supervised learning (see Beltrami, 2008) carried out using the one-month data recorded during January 2010.
The black continuous line in the lower graph of Fig. 2 shows the signal obtained by subtracting the tidal pattern f r o m the observations. This is the signal that shows the waveform of the actual tsunami. On the other hand, the grey continuous line shows the tsunami detected by the ANN algorithm. This signal is obtained by subtracting the ANN predictions f r o m the observa-tions. The tsunami reconstructed by the ANN algorithm has approximately the form of a N-wave (Tadepalli and Synolakis, 1994). Although the amplitude of this wave is sufficient for detection, i.e. it can exceed an opportunely chosen threshold, the form of the tsunami is not properly reconstructed. As already stated, this is due to the fact that the propagating tsunami influences the predictions by affecting the observation averages. The algorithm cannot automatically characterize the tsunami waveform. It is to be noticed that a very similar behavior w o u l d be observed in the case of the application of the DART algorithm.
3. DART and ANN algorithm modification
A possible and very simple way to make the DART and ANN algorithm capable of guaranteeing the automatic, real-time detection and characterization of a tsunami is that of lengthening the time interval between the actual and the prediction time. The
CM. Beltrami / Ocean Engineering 38 (20n) 1677-1685 1679 ro W -DARTak ''3 1 ^ Mara^ 0 6 -1 -1 - 1 3 1 0 9 7 A A A • 1 1 1 -DARTak ''3 1 ^ Mara^ 0 6 -1 -1 -1 V/-V 1 V 1 1 1 1 V/-0 3 / V/-0 6 V/-0 3 / V/-0 7 V/-0 3 / V/-0 8 V/-0 3 / V/-0 9 V/-0 3 / 1 V/-0 V/-0 3 / 1 1 V/-0 3 / 1 2 V/-0 3 / 1 3 V/-0 3 / 1 4 ra tt) 0 6 / 0 6 0 6 / 0 7 0 6 / 0 8 0 6 / 0 9 0 6 / 1 0 0 6 / 1 1 0 6 / 1 2 0 6 / 1 3 0 6 / 1 4 E" 1 0 2 / 2 3 0 2 / 2 4 0 2 / 2 5 0 2 / 2 6 0 2 / 2 7 0 2 / 2 8 0 3 / 0 1 0 3 / 0 2 0 3 / 0 3 time (days)
Fig. 1. Selected tracks of the used observation sets. Data are plotted in terms of sea level variation with respect to the mean sea level. The event that took place on February 27, 2010 following the Chilean earthquake is evident In the lower graph.
4 3 2 5 . 4 4 3 2 5 . 2 4 3 2 5 4 3 2 4 . 8 4 3 2 4 . 6 I-4 3 2 I-4 . I-4 - I r I I •a - BPR measures • b - A N N (5.25 min) • c - tide 0 6 : 3 0 0 7 : 0 0 0 7 : 3 0 0 8 : 0 0 0 8 : 3 0 0 9 : 0 0 0 9 : 3 0 1 0 : 0 0 1 0 : 3 0 1 1 : 0 0 1 1 : 3 0 0.4 0.2 0 - 0 . 2 h - 0 . 4 — a - c — a - b 0 6 : 3 0 0 7 : 0 0 0 7 : 3 0 0 8 : 0 0 0 8 : 3 0 0 9 : 0 0 0 9 : 3 0 10:00 1 0 : 3 0 1 1 : 0 0 1 1 : 3 0 time (hours)
Fig. 2. DART station 32412, February 27, 2010. In the upper graph the actual BPR measurennents (black continuous line) are plotted together with ANN algorithm predictions (grey continuous lines: prediction time set equal to 5.25 min in the future with respect to the time at which is centered the first average) and the tidal wave (black dashed line) obtained by filtering out the components with period lower than S h using a low-pass digital filter. In the lower graph, the de-tided series (black line) Is plotted with the series obtained by subtracting the ANN predictions from the observations (grey lines).
intent of such a lengthening is clearly that of delaying the moment at which a propagating tsunami influences the predic-tions by affecting the observation averages (in particular the first observation average). By way of example, setting the prediction time equal to 3 0 m i n and 1 5 s writh respect to the actual time (i.e. 3 5 . 2 5 m i n in the future w i t h respect to the time at w h i c h is centered the first average) makes i t possible to guarantee that the algorithm filtered signal gives a proper representation of tsuna-mis w i t h period w i t h i n the band 2 - 3 0 min. Such a modification can be easily carried out by calculating either the coefficients of the DART algorithm (Mofjeld, 1 9 9 7 ; Beltrami, 2 0 0 8 ) , or the adaptive weights of the ANN one (Beltrami. 2 0 0 8 ) using this
temporal parameter. By way of example Table 2 shows the DART algorithm's coefficients for different settings of the prediction time.
Fig. 3 shows the result of such a lengthening on the detection of the Chilean tsunami. In the upper graph, the continuous and dashed black lines represent the observations and the tidal pattern, and are equal to that shown i n Fig. 2 . The grey continuous line represents the ANN algorithm predictions, being the predic-tion time set equal to 3 5 . 2 5 m i n ift the future w i t h respect to the time at which is centered the first average. As it can be noticed, the ANN predictions tend to follow the tidal wave pattern, at least w i t h i n the prediction time interval (i.e. 3 0 min). As a consequence,
1680 CM. Beltrami / Ocean Engineering 38 (2011) 1677-1685 w i t h i n this interval, the algorithm is capable of a close
reconstruc-tion of the tsunami (lower graph of Fig. 3). In-fact, the filtered signal obtained by applying the ANN algorithm closely follows the actual tsunami signal. In this case, the tsunami is contempora-neously detected and characterized.
However, i t cannot be expected to get something for nothing. As i t w i l l be shown in the next section, lengthening the prediction time interval differently but invariably affects both the overall filtering performance of each algorithm and the extent to which an actually detected tsunami indirectly influences the filtered signal by affecting the observation averages.
4. Effects of the modification
As shown by Beltrami (2008), the prediction error of the DART algorithm depends both on the time interval p and on the magnitude of the disturbance to be filtered out. In the absence of background sea-noise, this disturbance is mainly caused by the tide. Departure from a perfectly filtered signal (a zero signal) therefore depends on the measurement location. For example, the filtered signals obtained by testing the algorithm on M2 tides of equal phase and different amplitudes show a residual oscillation of sinusoidal shape. Given an averaging interval p = 1 0 min, when the prediction time is set equal to 5.25 min, the range of this oscillation w i l l be approximately 0.26% of the tidal one. A t a location that experiences a tidal range of 2.0 m, an oscillation Table 2
The DART algorithm's coefficients for different settings of prediction time (sampling interval equal to 15 s).
Coefficient Prediction time 5.25 min Prediction time 35.25 min Wo -1- 1.16818457031250 4-2.45603613281250 w , -0.28197558593750 -2.72678027343750 W2 + 0.14689746093750 -H.67295214843750 W3 -0.03310644531250 -0.40220800781250
w i t h a range of 0.005 m is therefore expected to persist in the filtered signal. The residual oscillation range w i l l be augmented when the prediction time interval is lengthened. If the prediction time is set equal to 35.25 min, the range of this oscillation w i l l be approximately 2.54% of the tidal one. At a location that experi-ences a tidal range of 2.0 m, the range of the persisting oscillation w i l l be equal to 0.05 m, i.e. an order of magnitude greater than in the case of prediction time set equal to 5.25 min.
The way in which the adaptive weights are calculated makes the filtering performance of ANN algorithm dependent neither on the averaging interval p, nor on the observed signal range (Beltrami, 2008). Furthermore, such a performance is expected not to depend on the prediction rime interval, at least in theory. Actually, the efficiency of the supervised learning relies totally upon how accurately the training set represents all the possible disturbing fluctuations and their composition. If i t succeeds in this, the ANN algorithm error is expected to be nearly zero. This is especially so in the case of disturbing fluctuations consisting of regular wavy patterns such as the tidal one. Tests on M2 tides of equal phase and different amplitudes show that the range of the residual noise is in the order of 10'^% of the tidal one both i n the case of prediction time set equal to 5.25 min and i n the case of prediction time set equal to 35.25 min.
The actual influence of the prediction interval lengthening on the filtering performance o f both algorithms is shown in Figs. 4 and 5 by using short tracks of the observation sets already described i n Introduction. In particular. Fig. 4 shows a comparison of the filtering performance of the DART algorithm (grey line) w i t h that of the ANN one (black line) in the case of prediction time set equal to 5.25 min. In the figure, the left graphs show the filtered time series, while the right ones the corresponding amplitude spectra. As already observed by Beltrami (2008), neither the DART nor the ANN algorithm is capable of filtering out background pressure noise. Nevertheless, the closer predic-tion of both tidal and other regular oscillapredic-tions embedded i n the original pressure data makes the ANN algorithm capable of a better filtering performance. This is particulariy evident i n the
4325.4 4325.2 4325 4324.8 4324.6
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• a - BPR measures b - A N N (35.25 min) c - tide 4324.4 06:30 07:00 07:30 08:00 08:30 09:00 09:30 10:00 10:30 11:00 11:30 0.4 0.2 0 -0.2 -0.4 | ; 1 1 -•a - c n 1 ~ 06:30 07:00 07:30 08:00 08:30 09:00 09:30 10:00 10:30 11:00 11:30 time (hours)Fig. 3. DART station 32412. February 27. 2010. In the upper graph the actual BPR measurements (black continuous line) are plotted together with ANN algorithm predictions (grey continuous lines: prediction time set equal to 35.25 min in the future with respect to the time at which is centered the first average) and the tidal wave (black dashed line) obtained by filtering out the components with period lower than 8 h using a low-pass digital filter. In the lower graph, the de-tided series (black line) is plotted with the senes obtained by subtracting the ANN predictions from the observations (grey lines).
C M . Beltrami / Ocean Engineering 38 (2011) 1677-1685 1681 0.01 E -0.005 CO -0.01 Q. E
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10-10° 10^ 3 10-10-10 10-5 10- 10- 10-10-'' 10-3 .|o-2 frequency (Hz) 1 0 - 10-3 10-2 frequency (Hz) •• i i )l. i l i l :t t • • • • • • • • • • ' l - - ¬' " f t 'iftiia
: ; : ï : : : : ; : : : ; : : : • f . . t : 10-i ! ! 10-i f 10-i 10-i 10-i l 10-i • - • •• . . . .1 : : ::::!!: :::± . . . .1 : : " " • ' f • • • ! : • : Ï : : : ; 1 : : : : t : : : : : : : : 10-• I 10-• : : : : : : : : : : : :ï: :,J ::::::: , : : : : : ::±
•f : i l : : : : ' : : : : ; : : : : : : : ' : : : : : : : : : [ : t • • i : •10-Fig. 4. A comparison of the filtering performance of the DART algorithm (grey line) with that of the ANN one (black line) in the case of prediction time set equal to 5.25 min. Filtered time series (left graphs) and corresponding amplitude spectra (right graphs). Verrical dashed lines In the amplitude spectrum graphs show the limit of the period band 2-30 min.
two upper graphs of the figure, where the filtering performance of the DART and ANN algorithm is compared using the pressure observations recorded at the DART station al<73. It is to be noticed that the variation of the ANN algorithm filtered signals has a range approximately equal to 0.005 m, and that this variation is due to the background noise recorded by the device. In any case, the greater the tidal range, the greater the improvement of the filtering performance obtained by using the ANN algorithm.
Fig. 5 shows the same comparison in the case of prediction time set equal to 35.25 min. The overall worst performance of both the DART and ANN algorithm is evident. However, while the variation of the filtered signals resulting f r o m the application of the DART algorithm shows the previously stated strong depen-dency on the local tidal range that resulting from the application of the ANN one has a constant range of approximately 0.02 m. Therefore, although the ANN algorithm filtered signal is indepen-dent of the prediction time only theoretically, the range of its variability is quite limited i n all the cases. It is to be noticed that the network adaptive weights for each data-set resulted f r o m a supervised learning (see Beltrami, 2008) carried out using a one-month track of data. In particular, the supervised learning for station ak73 was carried out using the data recorded during October 1997 that for station d l 25 using the data recorded during May 2003, and that for station 32412 using the data recorded during January 2010.
Lets now address the problem of the extent to which an actually detected tsunami indirectly influences the filtered signal resulting f r o m the application of either the DART or the ANN algorithm by affecting the observation averages. The lower this influence, the greater the chance do detect (and possibly to characterize) tsunami events that may follow the leading one.
The upper graph of Fig. 6 shows the data recorded at DART station ak73 between 00:30 and 05:30 UTC on March 12, 1997 (black continuous line). A synthetic tsunami of m a x i m u m amplitude equal to 0.15 m and period equal to 22.5 m i n was superimposed to the original observations, starting at 01:00 UTC. The synthetic tsunami was derived on the basis of the N-wave by Tadepalli and Synolakis (1994). In the graph, the black dashed line refers to the tidal wave. These data were obtained, as before, by filtering out the components w i t h period shorter than 8 h f r o m the original record. The grey continuous line represents the DART algorithm prediction, being the prediction time set equal to 5.25 min. The black continuous line i n the lower graph of the same figure shows the signal obtained by subtracting the tidal pattern f r o m the observations. The grey continuous line shows the tsunami detected by the DART algorithm. As already seen in the case of the Chilean tsunami (Fig. 2), the tsunami reconstructed by the DART algorithm has the form of a N-wave (Tadepalli and Synolakis, 1994). Further—progressively lower—anomalies can be observed in the DART algorithm filtered signal around 02:15, 03:15 and 04:15 UTC. In-fact (Mofjeld, 1997), w h e n a tsunami is detected, the first and largest pulse shown by the filtered signal w i l l be invariably followed by further pulses. In the case of prediction time set equal to 5.25 min, such pulses w i l l occur during each of the subsequent 3 h, when the observation averages are affected by the recorded tsunami levels. An almost equal behavior would resulted f r o m the application of the ANN algorithm.
Figs. 7 and 8 show the resiflts of the application of the modified DART and ANN algorithm (prediction time set equal to 35.25 min) to exactly the same track of observations. The lower graph of Fig. 7 shows the filtered signal resulting from the
1682 C M . Beltrami / Ocean Engineering 38 (2011) 1677-1685 -0.04 00:00 12:00 00:00 12:00 00:00 0.04 E, 0.02 litu d 0 Q. E -0.02 CD -0.04 d125-June 08-09, 2003 00:00 12:00 00:00 12:00 00:00 time (hr) 0.04 0.02 0) 0 "5. E -0.02 CD -0.04 32412 - February 25-26, 2010 ; 00:00 12:00 00:00 12:00 00:00 time (hr) I Q O cu
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10-5 Q-E CD 10-10 . . . ; ! ! ! I I ! I I f ; ! - i t ' t t • i""'- Ï t •I -• -• -• -• -• 1-: 1-:1-:;1-:;1-:1-: 1-:1-:1-:1-:1-:1-: 10- 10- 10-:!:; :::¥: 10"'' 10-3 10-2 frequency (Hz) frequency (Hz) 10-! 10-! 10-! 10-! 10-! • 10-! . . 1 • 1. lii . . . . L. :::::: : : : :*:::: t ...f. - 5 10-" 10-3 10-2 10Fig. 5. A comparison of the filtering performance of the DART algonthm (grey line) with that of the ANN one (black line) in the case of prediction time set equal to 35.25 min. Filtered time series (left graphs) and corresponding amplitude spectra (nght graphs). Vertical dashed lines in the a.mplitude spectrum graphs show the limit of the period band 2-30 min.
4576 4575.5 4575 4574.5 4574 1 1 1 1 1 - I 1 1 ; -a - B P R me-asures • - - - • b - D A R T (5.25 min) - - - c - tide a - B P R measures • - - - • b - D A R T (5.25 min) - - - c - tide 1 l l l l 00:30 01:00 01:30 02:00 02:30 03:00 03:30 04:00 04:30 05:00 05:30 CD 0.3 0.2 0.1 0 -0.1 -0.2 1 • 1 1 1 1 a - c
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a - b:
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1 1 1 1 1 00:30 01:00 01:30 02:00 02:30 03:00 03:30 04:00 04:30 05:00 05:30 time (hours)Fig. 6. DART station ak73, March 12, 1997. In the upper graph the actual BPR measurements (black continuous line) with synthetic tsunami are plotted together with DART algorithm predictions (grey continuous lines: prediction time set equal to 5.25 min In the future with respect to the time at which is centered the first average) and the tidal wave (black dashed line) obtained by filtenng out the components with period lower than 8 h using a low-pass digital filter. In the lower graph, the de-tided series (black line) is plotted with the series obtained by subtracting the DART predicdons from the observadons (grey lines).
application of the DART algorithm (grey line). Although the upward shift w i t h respect to the tsunami itself. This is a filtered signal tends to follow the actual tsunami (black line), at consequence of the fact that the DART algorithm filtered signal least w i t h i n the prediction time interval, i t experiences an depends on the local tidal range. Actually, the upper-left graph of
CM Beltrami / Ocean Engineering 38 (2011) 1677-1685 1683 4576 4575.5 0) 4575 4574.5 4574 •a - BPR measures • b - DART (35.25 min), ' c - tide 00:30 01:00 01:30 02:00 02:30 03:00 03:30 04:00 04:30 05:00 05:30 0.3 0.2 0.1 0 -0.1 -0.2 l l l l l l l l a - b • : : : / a - b •
•
11
\ • ; : : : ^ / : : : ^' : : : 1 1 1 1 1 1 1 1 1 00:30 01:00 01:30 02:00 02:30 03:00 03:30 time (tiours) 04:00 04:30 05:00 05:30Fig. 7. DART station al<73, Marcti 12, 1997. In the upper graph the actual BPR measurements (black continuous line) with synthetic tsunanni are plotted together with DART algorithm predictions (grey continuous lines: prediction time set equal to 35.25 min in the future with respect to the time at which Is centered the first average) and the tidal wave (black dashed line) obtained by filtering out the components with period lower than 8 h using a low-pass digital filter. In the lower graph, the de-tided series (black line) is plotted with the series obtained by subtracting the DART predictions from the observations (grey lines).
4576 4575.5 \-0) 4575 I
ro
CD " 4574.5 •a - BPR measures b - ANN (35.25 min) ' c - tide - a - c - a - b 4574 00:30 01:00 01:30 02:00 02:30 03:00 03:30 04:00 04:30 05:00 05:30 0.3 0.2 0.1 0 -0.1 -0.2• i
1 ' • / 1i
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00:30 01:00 01:30 02:00 02:30 03:00 03:30 04:00 04:30 05:00 05:30 time (hours)Fig. 8. DART station al<73, March 12,1997. In the upper graph the actual BPR measurements (black continuous line) with synthetic tsunami are plotted together with ANN algorithm predictions (grey continuous lines: prediction time set equal to 35.25 min in the future with respect to the time at which Is centered the first average) and the tidal wave (black dashed line) obtained by filtering out the components with period lower than 8 h using a low-pass digital filter. In the lower graph, the de-tided series (black line) is plotted with the series obtained by subtracting the ANN predictions from the observations (grey lines).
Fig. 5 shows tliat around 01:00 UTC of March 12, 1997, the residual oscillation still present in the DART filtered signal reaches one of its maxima. It is this m a x i m u m that is responsible for the observed upward shift. Furthermore, the DART filtered signal shows that larger specular pulses follow the first one. Such pulses w i l l occur after 30 m i n and then during each of the subsequent 3 h, when the observarion averages are affected by the recorded tsunami levels. As far as the ANN algorithm is concerned, the lower graph of Fig. 8 shows the filtered signal
resulting f r o m its applicadon. In this case, the filtered signal (grey line) seems to perfecdy fit the actual tsunami (black line) w i t h i n the prediction time interval. Similar to the case of the Chilean tsunami (Fig. 3) the tsunami embedded in the ak73 observations is contemporaneously detected and characterized. Furthermore, after the specular pulse that follows the first one w i t h i n 30 min, the pulses that occur during each of the subsequent 3 h are progressively lower. In conclusion, the modified ANN algorithm allows for a contemporaneous detection and characterization of a
1684 C M . Beltrami / Ocean Engineering 38 (2011) 1677-1685 4325.4 4325.2 43^25 4324.8 4324.6 4324.4 / \ : ; ; ; i a - B P R measures b - D A R T (35.25 min) c - tide . i. i j ' I,,
\ f •
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.1,1: ; * : I : : '• '•
QC> ^ ^Ci ^ ^ 0 , ^ r ö ^ r | P ^^o;"? ^oi^ ^ö"? ^•^^ <t? ^^'^^ ^«i'? time (hours)
Fig. 9. DART station 32412, February 27, 2010. In the upper graph the actual BPR measurements (black continuous line) are plotted together with DART algorithm predictions (grey continuous lines: prediction time set equal to 35.25 min in the future with respect to the time at which is centered the first average) and the tidal wave (black dashed line) obtained by filtenng out the components with penod lower than 8 h using a low-pass digital filter. In the lower graph, the de-tided series (black line) is plotted with the senes obtained by subtracting the DART predictions from the observations (grey lines).
4325.4 4325.2 4325 4324.8 4324.6 4324.4 • a - B P R measures • b - A N N (35.25 min) ' 0 - tide . 0 ^ P 1 i 1 -•a - c a - b 0.4 0.2 0 -0.2 -0.4
,vO r^O r ö Ci^ ^ n^C) r^O
^Ci"? ^q;^ ^Ci^ ^CS^ ^K"? ^K'? ^q? ^üV^ ^^'^ ^t.;^ ^«ö'? time (hours)
Fig. 10. DART station 32412, February 27, 2010. In the upper graph the actual BPR measurements (black continuous line) are plotted together with ANN algorithm predictions (grey continuous lines: prediction time set equal to 35.25 min in the future with respect to the time at which is centered the first average) and the tidal wave (black dashed line) obtained by filtering out the components with period lower than 8 h using a low-pass digital filter. In the lower graph, the de-tided series (black line) is plotted with the series obtained by subtracting the ANN predictions from the observations (grey lines).
_ i I I I I i I i _
tsunami at all locations, whatever the tidal range, and at least limits the extent to which an actually detected tsunami indirectly influences the filtered signal by affecting the observation averages.
A confirmation of what has been stated so far comes f r o m the comparison between Figs. 9 and 10. The t w o figures respectively show the results of the application of the modified DART and ANN algorithm (prediction time set equal to 35.25 min) to the
CM. Beltrami / Ocean Engineering 38 (2011) 1677-1685 1685 observations recorded by the BPR of DART station 32412 on
February 27, 2010, between 09:00 and 16:00 UTC. This track of observations is particularly interesting as it shows how long the local sea level measurements may be influenced by a propagating tsunami. Due to the local low tidal range, also the filtered signal resulting from the application of the modified DART algorithm (Fig. 9) is capable of a good performance w i t h respect to both tsunami detection and characterization. However, the detected tsunami strongly influences the filtered signal after 30 m i n and then during each of the subsequent 3 h. On the other hand, the modified ANN algorithm (Fig. 10) allows for a contemporaneous detection and characterization of the tsunami w i t h i n the predic-tion time interval, and at least limits the extent to which i t influences the subsequent filtered signal. In any case, i f the tsunami was followed by other events at an interval greater than the prediction time (30 min, i n the discussed case), these further waves would be neither clearly detected nor properly characterize.
5. Conclusion
A simple modification of the DART (IVIofjeld, 1997) and ANN algorithm (Beltrami, 2008) capable of guaranteeing the auto-matic, real-time detection and characterization of a tsunami was investigated. The modification consists i n lengthening the time interval between the actual and the prediction time, being the intent that of delaying the moment at which a possible propagating tsunami influences the predictions and therefore the algorithm' filtered signals. Tests carried out using actually measured time series show that setting the prediction time equal to 30 m i n and 15 s w i t h respect to the actual time makes i t possible to guarantee that the algorithms' filtered signal gives a proper representation of tsunamis w i t h period w i t h i n the band 2-30 min. This is particularly true for the ANN algorithm filtered signal, as it is not subject to the tide-dependent residual oscilla-tion inherently present i n the DART algorithm one. However, lengthening the prediction time interval differently but invariably affects the extent to which an actually detected tsunami indir-ectly influences the filtered signal by affecting the observation averages. Therefore, i f the tsunami was followed by other events at a time interval greater than the selected prediction time (equal to 30 m i n in the discussed case), these further waves would be neither clearly detected nor properly characterize. I n any case, when a short distance separates the measurement location f r o m the coast of interest, the automatic, real-time tsunami detection and characterization w i l l be the main concern. In these situation, such a contemporaneous detection and characterization are actually essential in order to guarantee both a timely warning
and a correct level of tsunami alert. Furthermore, the modified either DART (at low tidal range location) or ANN algorithm can be always coupled w i t h the standard version of one of the two algorithms in order to guarantee at least the detection of possible tsunami events that may follow the first one at an interval greater than the prediction time one. It is finally to be stressed that the length of the interval between the actual and the prediction time can be clearly extended to the upper limits of the tsunami period band (around 40 min). In this case, the effect on the filtering performance of the DART algorithm w i l l be augmented, as well as the influences on the filtered signal of both the algorithms caused by a detected tsunami.
Acloiowledgments
This work was carried out under the research project PRIN2007 (prot. 2007MNBEMY) led by Prof. Paolo De Girolamo and funded by the Italian Ministry for University and Scientific Research (MlUR).
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