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On the performance of sequential Bayesian update for database of diverse tsunami scenarios

Reika Nomura, Louise A. Hirao Vermare, Saneiki Fujita, Donsub Rim, Shuji Moriguchi, Randall J. LeVeque, Kenjiro Terada

TL;DR

This work evaluates a sequential Bayesian tsunami-scenario-detection framework on a diverse database of complex fault-slip patterns, comparing scenario superposition (weighted mean) with the prior most-likely method and benchmarking against DTW. It leverages proper orthogonal decomposition (POD) to extract wave-history features and updates posterior probabilities via a Mahalanobis-distance-based likelihood, applied to 1771 Westport Cascadia scenarios filtered from a larger synthetic dataset. Key findings show that a 3–4 minute observation window generally suffices for accurate predictions; the weighted-mean approach improves inundation-trend predictions but does not consistently beat the most likely method or the DTW benchmark, highlighting limitations in the current probabilistic update for scenario superposition. The study suggests reformulating the probability update to treat multiple scenarios as simultaneous contributors, which could unlock more accurate and timely tsunami risk assessments for evacuation planning in diverse, real-world settings.

Abstract

Although the sequential tsunami scenario detection framework was validated in our previous work, several tasks remain to be resolved from a practical point of view. This study aims to evaluate the performance of the previous tsunami scenario detection framework using a diverse database consisting of complex fault rupture patterns with heterogeneous slip distributions. Specifically, we compare the effectiveness of scenario superposition to that of the previous most likely scenario detection method. Additionally, how the length of the observation time window influences the accuracy of both methods is analyzed. We utilize an existing database comprising 1771 tsunami scenarios targeting the city Westport (WA, U.S.), which includes synthetic wave height records and inundation distributions as the result of fault rupture in the Cascadia subduction zone. The heterogeneous patterns of slips used in the database increase the diversity of the scenarios and thus make it a proper database for evaluating the performance of scenario superposition. To assess the performance, we consider various observation time windows shorter than 15 minutes and divide the database into five testing and learning sets. The evaluation accuracy of the maximum offshore wave, inundation depth, and its distribution is analyzed to examine the advantages of the scenario superposition method over the previous method. We introduce the dynamic time warping (DTW) method as an additional benchmark and compare its results to that of the Bayesian scenario detection method.

On the performance of sequential Bayesian update for database of diverse tsunami scenarios

TL;DR

This work evaluates a sequential Bayesian tsunami-scenario-detection framework on a diverse database of complex fault-slip patterns, comparing scenario superposition (weighted mean) with the prior most-likely method and benchmarking against DTW. It leverages proper orthogonal decomposition (POD) to extract wave-history features and updates posterior probabilities via a Mahalanobis-distance-based likelihood, applied to 1771 Westport Cascadia scenarios filtered from a larger synthetic dataset. Key findings show that a 3–4 minute observation window generally suffices for accurate predictions; the weighted-mean approach improves inundation-trend predictions but does not consistently beat the most likely method or the DTW benchmark, highlighting limitations in the current probabilistic update for scenario superposition. The study suggests reformulating the probability update to treat multiple scenarios as simultaneous contributors, which could unlock more accurate and timely tsunami risk assessments for evacuation planning in diverse, real-world settings.

Abstract

Although the sequential tsunami scenario detection framework was validated in our previous work, several tasks remain to be resolved from a practical point of view. This study aims to evaluate the performance of the previous tsunami scenario detection framework using a diverse database consisting of complex fault rupture patterns with heterogeneous slip distributions. Specifically, we compare the effectiveness of scenario superposition to that of the previous most likely scenario detection method. Additionally, how the length of the observation time window influences the accuracy of both methods is analyzed. We utilize an existing database comprising 1771 tsunami scenarios targeting the city Westport (WA, U.S.), which includes synthetic wave height records and inundation distributions as the result of fault rupture in the Cascadia subduction zone. The heterogeneous patterns of slips used in the database increase the diversity of the scenarios and thus make it a proper database for evaluating the performance of scenario superposition. To assess the performance, we consider various observation time windows shorter than 15 minutes and divide the database into five testing and learning sets. The evaluation accuracy of the maximum offshore wave, inundation depth, and its distribution is analyzed to examine the advantages of the scenario superposition method over the previous method. We introduce the dynamic time warping (DTW) method as an additional benchmark and compare its results to that of the Bayesian scenario detection method.
Paper Structure (18 sections, 18 equations, 11 figures, 1 table)

This paper contains 18 sections, 18 equations, 11 figures, 1 table.

Table of Contents

  1. Introduction
  2. Sequential tsunami scenario detection
  3. POD for extracting the tsunami characteristics
  4. Bayesian update
  5. Tsunami scenario detection
  6. Most probable scenario
  7. Weighted mean scenario
  8. Shortest DTW distance scenario
  9. Diverse tsunami scenario database
  10. Synthetic tsunami scenario database comprising diverse and complex fault rupture patterns
  11. Observation time window setup
  12. Results of scenario detection with various observation time windows
  13. Wave history data $\eta^{\max}_{n',\chi}$
  14. Maximum inundation depth $H_{\max}$
  15. Inundation distribution $\bm{h}_{\max}$
  16. ...and 3 more sections

Figures (11)

  • Figure 1: Location of the city of Westport and the observation gauges. (a-c) Westport is a coastal city located in Washington state, approximately 100 km from the Cascadia subduction zone. (d) Topography elevation on the Westport Peninsula.
  • Figure 2: a The CSZ fault region with a sample heterogeneous slip distribution (from the open repository UW_repo that summarizes the data used in Williamson et al. 2020 williamson2020source), b The cumulative contribution $\textrm{c}(r)$ defined in Eqn. \ref{['eq:contribution']}.
  • Figure 3: a Wave history data and its wave arrival time $t_{arrv}$. b Histograms of the scenarios based on the first wave arrival time. The colors and hatching denote the magnitude of the local maximum inundation depth. $H_{\max}$.
  • Figure 4: The results of maximum wave height $\eta_{n',\chi}^{\max}$ detection. (a), (b), and (c) show the predictions based on the most likely scenario \ref{['eq:eta_most']} for observation time windows of $t_{obs}$ =1 min, 8 min, and 15 min, respectively. (d), (e), and (f) show the predictions based on the weighted mean scenario \ref{['eq:eta_mean']} for observation time windows of $t_{obs}$ =1 min, 8 min, and 15 min, respectively.
  • Figure 5: The variance in the maximum wave height prediction error at Gauge 130 during each observation period $t_{obs}$. (a) Results based on most likely scenario detection, and (b) results based on the weighted mean scenario. The diamond plot, horizontal line inside the box, and edge lines of the whiskers represent the mean, median, and min/max values, respectively.
  • ...and 6 more figures