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1 Song, J., & Goda, K. (2015). Sensitivity of probabilistic tsunami loss estimation to stochastic source modelling. Paper presented at 13th International Probabilistic Workshop, Lierpool, United Kingdom. License (if available): Unspecified Link to publication record in Explore Bristol Research PDF-document University of Bristol - Explore Bristol Research General rights This document is made available in accordance with publisher policies. Please cite only the published version using the reference above. Full terms of use are available:

2 SENSITIVITY OF PROBABILISTIC TSUNAMI LOSS ESTIMATION TO STOCHASTIC TSUNAMI MODELLING Abstract JIE SONG 1 and KATSUICHIRO GODA 2 1 Department of Civil Engineering, University of Bristol, University Walk, Bristol, UK. Jie.Song@bristol.ac.uk 2 Department of Civil Engineering, University of Bristol, University Walk, Bristol, UK. Katsu.Goda@bristol.ac.uk A new probabilistic tsunami risk assessment framework is proposed, consisting of three components: (1) tsunami hazard modelling based on inversion-based stochastic source models and Monte Carlo tsunami simulation; (2) tsunami fragility assessment, and (3) tsunami loss estimation. The risk assessment results are uncertain because of various assumptions and approximations. The first component enables generation of a large number of random earthquake slip distributions and consequently facilitates the consideration of uncertainty in inverted source models. This study investigates the uncertainty propagation from stochastic source models to probabilistic loss estimation, focusing on the 2011 Tohoku, Japan tsunami as a case study from a retrospective viewpoint. The variability of final loss prediction is demonstrated by various visualisation methods. Keywords: Tsunami; uncertainty; risk; vulnerability; visualisation. Introduction Tsunami is a series of travelling waves of long wave-length and period, initiated by the sudden deformation of sea-floor. The wave height increases greatly when the wave travels from deep sea to shallow water. As a secondary hazard triggered by the main-shock of an earthquake, tsunami can cause tremendous damage to the inundated coastal areas. The most recent 2011 Tohoku tsunami has revealed an underestimation of tsunami risk along the Tohoku coast in Japan, although Tohoku was thought a region of high seismic and tsunami risk and thus was well prepared for tsunamis (Mori et al., 2011). The preparation turned out to be significantly insufficient, with a high proportion of tsunami barriers severely damaged and thus could not serve their functions, resulting in a huge amount of economic and human loss (Fraser et al., 2013). Therefore, the tsunami risk assessment is important for effective tsunami risk reduction countermeasures. Although the uncertainty underlying in the process of catastrophe risk modelling is inevitable, the treatment of uncertainty is fragmented into separate steps Proc. of the 13th International Probabilistic Workshop (IPW 2015) Edited by Edoardo Patelli & Ioannis Kougioumtzoglou Copyright c 2015 IPW 2015 Organisers :: Published by Research Publishing ISBN: doi: /

3 Proc. of the 13th International Probabilistic Workshop (IPW 2015) of tsunami risk assessment (e.g. earthquake source characterisation). The investigation into how uncertainty propagates in the procedure of tsunami risk assessment can help improve the accuracy and reliability of the assessment results and thus promote the the informed decision making with regards to tsunami risk reduction in terms of hard measures as well as soft measures. Different stakeholders have different concerns about hazard/risk information, so understanding the importance of uncertainty in tsunami risk modelling is beneficial for decision making for different purposes. This study aims to quantify the influence of uncertainty in tsunami modelling on probabilistic tsunami loss estimation. Current state-of-the-practice regional tsunami hazard maps, which are prepared based on tsunami hazard parameters corresponding to a single scenario on a single fault, are unable to reflect the variability in different scenarios and thus fail to deal with the uncertainty in hazard prediction. For instance, the tsunami caused by the 2011 Tohoku earthquake exceeded the historical scenarios considered for preparation of tsunami hazard maps, as a consequence of underestimation of uncertainty. The variability in different tsunami scenarios can be shown in stochastic tsunami inundation depth maps which are generated by taking into account of a large number of tsunami slip models. The major sources of uncertainty in tsunami hazard intensity prediction are resulted from earthquake source characteristics such as fault geometry and slip distribution (McCloskey et al., 2008; Løvholt et al., 2012; Fraser et al., 2014; Goda et al., 2014; Wiebe and Cox, 2014). In order to evaluate the variability of different tsunami source models in tsunami inundation height prediction, Monte Carlo tsunami simulation is conducted based on synthesised stochastic source models developed by the approach to generating a large number of possible scenarios with different fault geometries and earthquake slips proposed by Mai and Beroza (2002). This allows the consideration of epistemic uncertainty in stochastic source models by incorporating multiple reference source models (Goda et al., 2014). As a result, stochastic inundation depth maps can be produced, and then tsunami risk maps which show the exceedance probability of a certain damage state can be generated accordingly in combination with tsunami fragility functions. The uncertainty in different earthquake source models is visualised by showing the variability of probabilistic tsunami loss. Moreover, the fragility curves should be appropriately selected from a pool of curves with different characteristics. The reliability of selected fragility curves for application with necessary assumptions is uncertain, because performance of structures of different heights, construction materials and seismic codes in different regions is varied. However, the insufficiency of existing tsunami fragility curves may result in more presumptions and thus increase the uncertainty in reliability of risk assessment results. Probabilistic Tsunami Risk Assessment Framework A generic probabilistic tsunami risk assessment framework is divided into three major components: stochastic tsunami hazard modelling, tsunami fragility assessment, and tsunami damage analysis. Uncertainty exists in every component and the contribution of each source of uncertainty to the tsunami loss estimation has not been understood. The framework is focused 85

4 Edoardo Patelli & Ioannis Kougioumtzoglou (editors) on the 2011 Tohoku tsunami as a case study to evaluate the uncertainty propagation in tsunami risk assessment. Stochastic Tsunami Hazard Modelling The new methodology for generation of stochastic earthquake source models is based on the approach developed by Mai and Beroza (2002) through spectral analysis of slip heterogeneity of inverted tsunami source models and spectral synthesis of random slip fields. Goda et al. (2014) have extended the method to large mega-thrust subduction earthquakes such as 2011 Tohoku earthquake, which enables generation of a large set of earthquake scenarios having varied earthquake slips and fault geometries. In order to account for different potential slip distributions for a given scenario (i.e. a M w 9-class tsunamigenic event), multiple tsunamigenetic earthquake source models can be employed in Monte Carlo simulation. Therefore, the simulation results can reflect the uncertainty and variability in the rupture process of megathrust earthquakes. The ranges of different geometrical properties (i.e. top-edge, strike, and dip) are determined by inspection of various inversion-based models and the seismotectonic setting in the Tohoku region. Only one parameter is changed at a time by keeping the slip distribution identical to the source model and an average value of all the variations of each geometrical parameter is used as a representation. The Monte Carlo tsunami simulation can be conducted based on a well-tested numerical code of Goto et al. (1997) which evaluates non-linear shallow water equations using a leap-frog staggered-grid finite difference scheme for generation of off-shore tsunami propagation and run-up. Subsequently, the tsunami inundation depth can be computed by a moving boundary approach in which a dry or wet condition of a computational cell is determined by the total water depth relative to its elevation. Formulae by Okada (1985) and Tanioka and Satake (1996) are used for determination of initial surface elevation, with different boundary conditions resulted from stochastic earthquake slip models. As a result, varied tsunami inundation depths are simulated for all the generated slip models. Tsunami Fragility and damage assessment In tsunami risk assessment, fragility curves which are generated based on damage statistics from post-event survey or computational simulation, provide the exceedance probability attaining a certain damage state (DS) given a tsunami intensity. Generally, the fragility is expressed as: ( ) ln(x) mr F R (x) = Φ where Φ is the cumulative normal distribution function; x is the intensity measure (IM), and tsunami inundation depth/height is most commonly used because the measurement is relatively straightforward;m R andξ R are median (in units that are dimensionally consistent with demand ξ R (1) 86

5 Proc. of the 13th International Probabilistic Workshop (IPW 2015) ln(x)) and logarithmic standard deviation of damage state capacity in terms of IM, respectively. Similar to seismic risk assessment, the proper selection of vulnerability curves is very important for tsunami risk assessment. Unlike earthquake vulnerability functions which have been extensively developed for all kinds of structure types using an empirical as well as analytical method in different regions, far less fragility functions for tsunami have been developed so far. Empirical tsunami fragility curves have been developed by Suppasri et al. (2013) based on damage surveys of the 2011 Tohoku tsunami, which cover four types of building materials (i.e. reinforced concrete, steel, wood and masonry), different numbers of stories and two different coastal topographies (i.e. plain and ria coast). Although the posttsunami survey is regarded as the most realistic source of loss statistics, the application of empirical fragility functions for potential loss prediction is substantially constrained to the region where the data were collected or possibly similar subduction regions. Besides, the performance of similar structure types in different regions can be very different as well under same tsunami conditions (Suppasri et al., 2013). Meanwhile, for tsunami prone areas where no sufficient data have been collected, currently few analytical tsunami functions are available in the literature (Macabuag et al., 2014). Therefore, the tsunami loss prediction may involve more uncertainty because of the significantly small pool of available tsunami fragility functions when the existing ones are applied to regions with different asset characteristics. A unique characteristic of tsunami damage is that buildings have experienced the ground shaking before tsunami waves, so the final damage of a structure is actually an accumulation of damage due to both main-shock and tsunami waves in sequence. Therefore, tsunami vulnerability of structures should be analysed under a multi-hazard framework by considering the damage contribution of both ground motion and tsunami. Despite the lack of such fragility models, an attempt to take into account the interaction of main-shock and subsequent tsunami has been made by Park et al. (2012). Their study suggested that there is a substantial difference considering tsunami as an independent hazard or secondary hazard in terms of collapse vulnerability of structures. Thus further investigation is required to assess how important the two-phase loading is to analytical tsunami fragility derivation by comparison to the empirical ones and consequently how sensitive the tsunami loss estimation is to this difference. With both tsunami hazard and fragility information prepared, the exceedance probability p(ds i ) of a given damage state among totalndamage states for all the simulated scenarios can be calculated and transformed into stochastic tsunami risk maps. By synthesising the damage probabilities with replacement costc R and loss ratiosr L (ds i ), the final economic loss can be estimated by: n L = C R p(ds i )R L (ds i ) (2) i=1 87

6 Edoardo Patelli & Ioannis Kougioumtzoglou (editors) Case Study and Uncertainty Propagation The 2011 Tohoku earthquake provides an unprecedented opportunity for validation of numerical source models, because abundant and various forms of observation records, such as inundation depths and tsunami damage data, are available. The objective of this section is to show the contribution of variability of tsunami source models in tsunami hazard modelling to loss prediction variability, focusing on a coastal city Rikuzentakata (see Fig 1) which was one of the most severely impacted cities by the 2011 Tohoku event (Fraser et al., 2013). In this study, eleven published inversion-based source models are used to generate stochastic slip models (Ammon et al., 2011; Fujii et al., 2011; Hayes, 2011; Iinuma et al., 2011, 2012; Shao et al., 2011; Yamazaki et al., 2011; Gusman et al., 2012; Satake et al., 2013). A total number of 726 slip distributions, including 50 stochastic slip distributions and 16 geometry variations for each reference model, are generated for Monte Carlo tsunami simulation. A building portfolio of Rikuzentakata, consisting a high proportion of 4963 wood structures in addition to 143 RC structures, 265 steel structures and 743 masonry structures, is employed for damage and loss assessment. The cost models employed are log-normal distribution, with mean and coefficient of variation obtained from regional building data statistics provided by the Ministry of Land, Infrastructure, and Transportation (MLIT). Fig. 1. Tohoku coastline Using the simulation results of 726 stochastic slip models based on the eleven reference models, stochastic inundation depth maps can be produced, which show the maximum tsunami inundation depth for given percentile levels by ranking 726 scenarios. Fig. 2 shows a set of stochastic tsunami hazard maps of inundation area above 1 m in comparison with observation 88

7 Proc. of the 13th International Probabilistic Workshop (IPW 2015) Fig. 2. Stochastic inundation depth maps in terms of area above 1 m data according to tsunami inundation and run-up survey results from the Tohoku Tsunami Survey (TTJS) team (Mori et al., 2011). A typical case (i.e. 50th percentile) and rare cases (i.e. 10th and 90th percentiles) are considered. It can be noticed that the 10th percetile map does not agree with observation data very well, while the difference in maps of the 50th percentile and 90 percentile is insignificant. In combination with available tsunami fragility functions (Suppasri et al., 2013) and building inventory for the area of interest, the stochastic tsunami hazard maps can be transformed into damage probability maps for any given damage state. The stochastic collapse probability maps of 10th, 50th and 90th percentile levels corresponding to maps in Fig. 2, which synthesise the local tsunami hazard level and structural vulnerability, are shown in Fig. 3. Compared to the significant difference between tsunami inundation depth maps of 10th percentile and 50th percentile, the difference between the corresponding collapse probability maps of these two percentile levels is small. Besides, a substantially large patch of green markers can be noticed in the 90th percentile collapse probability map, while such feature is not reflected in other two percentile maps. These comparisons show that the major difference in tsunami hazard maps falls between 10th and 50th percentile levels, while that in collapse damage probability maps lies between 50th and 90th percentile levels. This implies that the variability of spatial damage probability for this particular damage state (i.e collapse) does not follow the same trend of the variability of inundation depth distribution by using different tsunami source models. The variability of wash-away damage probability maps (see Fig. 4) is similar to that of collapse probability maps. The wash-away probability across the region is concentrated in a high probability range (i.e ), which is validated by the fact that almost all wood structures (main structure type) in this area were destroyed in the 2011 Tohoku tsunami (Fraser et al., 2013). Overall, the spatial damage probability estimation is less sensitive to uncertainty in tsunami source characterisation than prediction of tsunami hazard distribution. Since wood structures are the vast majority in the building portfolio of Rikuzentakata and main building materials for residential buildings in Japan, the cumulative probability distribution functions of the number of collapsed wood structures are plotted in Fig. 5 (left), 89

8 Edoardo Patelli & Ioannis Kougioumtzoglou (editors) Fig. 3. Stochastic collapse probability maps Fig. 4. Stochastic wash-away probability maps Fig. 5. Cumulative probability distribution functions of the number of collapsed wood structures (left) and total tsunami loss (right) 90

9 Proc. of the 13th International Probabilistic Workshop (IPW 2015) showing the variability among the eleven reference models at the same time. Overall, all the curves follow the same trend compared with the mean curve (shown in thick solid line), and the difference among different source models generally becomes smaller with the increase of probability. Substantially wide variation exists at low probability levels. The difference between the maximum and minimum value at a median probability level can be as large as approximately 1000 structures which is more than one quarter of the total number of wood structures in the portfolio. This may indicate that the application of a single slip model for tsunami hazard assessment can lead to relatively large error in loss estimation. Such analyses can be repeated for all types of structures and all damage states for prediction of the overall tsunami loss for a given building portfolio. The right graph in Fig. 5 shows probabilistic tsunami loss incorporating all four types of buildings and all damage states defined in the empirical tsunami fragility functions, presenting a similar trend to the left graph. Conclusions This paper proposed a comprehensive tsunami risk assessment framework to investigate the uncertainty propagation of major modelling components, focusing on the influence of different tsunami source models on probabilistic tsunami loss estimation. The variability of probabilistic tsunami loss resulted from tsunami source characterisation was visualised and quantified through a detailed case study using 726 stochastic slip distributions based on eleven inverted source models for the 2011 Tohoku tsunami. These results are beneficial to decision makers and local residents with regard to the uncertainty in tsunami hazard level prediction for different risk mitigation purposes. As a secondary hazard of main-shock, the influence of initial damage resulted from ground shaking on tsunami vulnerability and the contribution of uncertainty due to interaction of two hazards is still unclear and needs further research. References C. J. Ammon, T. Lay, H. Kanamori, and M. Cleveland. A rupture model of the 2011 off the Pacific coast of Tohoku earthquake. Earth, Planets and Space, 63(7): , S. Fraser, A. Raby, A. Pomonis, K. Goda, S. C. Chian, J. Macabuag, M. Offord, K. Saito, and P. Sammonds. Tsunami damage to coastal defences and buildings in the March 11th 2011 Mw 9.0 Great East Japan earthquake and tsunami. Bulletin of Earthquake Engineering, 11 (1): , S. A. Fraser, W. L. Power, X. Wang, L. M. Wallace, C. Mueller, and D. M. Johnston. Tsunami inundation in Napier, New Zealand, due to local earthquake sources. Natural Hazards, 70 (1): , Y. Fujii, K. Satake, S. Sakai, M. Shinohara, and T. Kanazawa. Tsunami source of the 2011 off the Pacific coast of Tohoku earthquake. Earth, Planets and Space, 63(7): , K. Goda, P. M. Mai, T. Yasuda, and N. Mori. Sensitivity of tsunami wave profiles and inun- 91

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