TSUNAMI HAZARD AND CASUALTY ESTIMATION MODEL

Transcription

1 10NCEE Tenth U.S. National Conference on Earthquake Engineering Frontiers of Earthquake Engineering July 21-25, 2014 Anchorage, Alaska TSUNAMI HAZARD AND CASUALTY ESTIMATION MODEL Harry Yeh 1 ABSTRACT In the event of earthquakes, human losses directly relate to the extent of damage to buildings, which is strongly correlated with the earthquake magnitude. With little forewarning time, a majority of casualties result from crushing or suffocation associated with structure collapse. In contrast, there is some lead-time for tsunamis allowing for evacuation. This makes a significant difference in consideration for casualty estimation. Data from historical tsunami events strongly suggest that tsunami s flow condition is not the controlling factor for determining the fatality rate. It appears that instead of physical tsunami severity, critical factors for determining tsunami impacts on humans are effectiveness of tsunami warning systems and education that motivates people to evacuate in a timely manner. Based on the foregoing observations, we propose a methodology to estimate tsunami casualty losses. The methodology allows us to make judgment for uncertain factors associated with human behaviors, and computes the number of both fatalities and injuries in a rational manner. The methodology is now incorporated into the prototype version of tsunami MH HAZUS. 1 Edwards Professor, School of Civil & Construction Engineering, Oregon State University, Corvallis, OR Yeh, H. Tsunami hazard and casualty estimation model. Proceedings of the 10 th National Conference in Earthquake Engineering, Earthquake Engineering Research Institute, Anchorage, AK, 2014.

2 10NCEE Tenth U.S. National Conference on Earthquake Engineering Frontiers of Earthquake Engineering July 21-25, 2014 Anchorage, Alaska Tsunami Hazard and Casualty Estimation Model Harry Yeh 1 ABSTRACT In the event of earthquakes, human losses directly relate to the extent of damage to buildings, which is strongly correlated with the earthquake magnitude. With little forewarning time, a majority of casualties result from crushing or suffocation associated with structure collapse. In contrast, there is some lead-time for tsunamis allowing for evacuation. This makes a significant difference in consideration for casualty estimation. Data from historical tsunami events strongly suggest that tsunami s flow condition is not the controlling factor for determining the fatality rate. It appears that instead of physical tsunami severity, critical factors for determining tsunami impacts on humans are effectiveness of tsunami warning systems and education that motivates people to evacuate in a timely manner. Based on the foregoing observations, we propose a methodology to estimate tsunami casualty losses. The methodology allows us to make judgment for uncertain factors associated with human behaviors, and computes the number of both fatalities and injuries in a rational manner. The methodology is now incorporated into the prototype version of Tsunami MH HAZUS. Introduction Tsunami-risk areas are limited to narrow strips along the shoreline (less than a few kilometers from the shoreline). Within the inundation zones, damage and losses are not uniform: usually, the nearer the shoreline, the higher the tsunami power. Such characteristics are different from other hazards such as earthquakes, river floods, and hurricanes. Because tsunamis are rare and because forewarning of tsunami arrival is possible, the primary mitigation tactic is evacuation. The forewarning times for river floods and hurricanes are much longer than the available times for local tsunamis; hence evacuation strategies would be different from tsunami cases. Such forewarning for evacuation is impractical for earthquakes. The primary focus on earthquake mitigation is to prevent buildings from collapse, because a majority of earthquake casualties are due to crushing and/or suffocation by structure collapse. The 2004 Indian Ocean Tsunami took almost 230,000 lives [1]. The 2011 East Japan Tsunami killed people and injured 6,147 people; 2636 people are still missing as of February [2]; 94.5% of the total death count is attributed to drowning; only 1.2% of fatalities were caused by the earthquake [3] and the rest were by fires, landslides, and disease. Although we anticipate similar statistics for a similar extraordinary tsunami event, it should be cautioned that outcomes could be different for a smaller tsunami event. 1 Edwards Professor, School of Civil & Construction Engineering, Oregon State University, Corvallis, OR Yeh, H. Tsunami hazard and casualty estimation model. Proceedings of the 10 th National Conference in Earthquake Engineering, Earthquake Engineering Research Institute, Anchorage, AK, 2014.

3 Background Suppasri et al. [4] compiled data on fatality rate (fatality rate is the ratio of the number of people killed to the total population in the inundation area) for many historical tsunami events: see Fig. 1. The figure note the log-log scales reveals that tsunami s flow condition (represented by maximum runup heights) is not the controlling factor determining the fatality rate. Consider the 0.015% fatality rate data point at a 2.5 m tsunami runup height as found in Fig. 1. At a similar runup height (3 ~ 3.5 m), a data point exists showing the fatality rate at about 50%, an increase by more than 3 orders of magnitude. Another example is a comparison of nearly 100% fatality rate at the 5 m tsunami runup height with the 0.06% fatality rate at the tsunami runup height of 31 m. Evidently tsunami runup height alone is not a good indicator when estimating fatality rate. The figure provides, however, one important point, which is that the tsunami fatality rate diminishes when the maximum tsunami height is less than 1.5 m. Note that tsunami runup height is the elevation from the sea level; the actual inundation depth at a location of interest is usually smaller than the height. In the same paper [4], Suppasri et al. presented better correlation between fatality rate and housing damage rate than the correlation between fatality rate and tsunami runup height for the event of 2011 East Japan Tsunami. This trend makes sense because humans dwell in houses. Nonetheless, the results are for a specific tsunami event in a specific locality (Miyagi Prefecture). Careful examination for each tsunami event presented in Fig. 1 evidently indicates that such a correlation cannot be used for the prediction of fatality rate in a different locality caused by a different tsunami event. Figure 1. Tsunami fatality rate vs. maximum tsunami runup height of historical events (data were provided by Suppasri).

4 It is therefore believed that critical factors for determining tsunami impacts on humans are effective education and effective warning. To determine the casualty rate, we note the following: Without warning (including a natural cue = ground shaking), nobody would start to evacuate until one detects the tsunami near the shore. Coastal communities who are adequately prepared for tsunamis would respond to the warning quicker than those who are not prepared. People would respond slower when they receive tsunami warning for a distant tsunami than for a local one. There is always a possibility that a few people behave in an unpredictable fashion. Evacuation speed depends on a) age and gender, b) ambient condition, c) obstacles created by earthquake. Important physical factors are how fast and how far the tsunami advances inland. A shorter evacuation distance to a safe haven results in a better chance of survival. Human behaviors and actions under strained conditions are difficult to predict. One of the most systematic and logical methodologies for a tsunami scenario is agent-based modeling [5]. In agent-based modeling, a system is modeled as a collection of autonomous decision-making agents. An individual agent evaluates the situation and makes decisions based on a set of rules. Agent-based simulations for tsunamis have been performed in the past, for the town of Owase, Japan [6], for Long Beach Peninsula, Washington [7], and for the town of Cannon Beach, Oregon [8]. Agent-based modeling requires detailed spatiotemporal data of tsunami inundation processes, in addition to geospatial data such as road networks, locations and operations of warning transmissions, and demographic data. Also needed is social information for how people respond to the warning and interact with other evacuees, and how people are killed and injured (casualty modeling). Here we adapt the concept of agent-based modeling that can be implemented in a simplified manner. The methodology presented here is as rational as possible even though the outcomes are strongly determined by human s decision-making and behaviors. Unlike physical laws governed in fluid flows and structural behaviors, human behaviors are not controlled by clear laws but must be estimated by their tendencies (both based on empirical data and hypotheses). Therefore, the methodology is necessarily designed such that the users are allowed to make their own judgment calls for the characterization of a community, and human behaviors of the residents and visitors. Methodology For the sake of simplification, only pedestrian evacuation is considered, and possibilities of other evacuation means such as automobiles, bikes, boats, etc. are excluded; also excluded is a possibility of evacuation to tall and tsunami-resistant buildings. Instead of tracking each individual evacuee, we divide a community of interest into population blocks (e.g. census or city blocks): each block represents similar conditions for evacuation. For a given tsunami event, required data for our casualty-rate assessment are: a) DEM (Digital Elevation Model) and demographic information for each population block. b) Evacuation distance that can be expressed by tortuosity C t (the ratio of the evacuation route length to the direct distance between two points). For example, when the route is perfectly zigzagged with right angles in the square pattern, then theoretically C t = 2. c) Location of maximum tsunami penetration Max X (= max runup contour line). d) Tsunami arrival time T 0 and the time of maximum tsunami penetration T max.

5 e) Warning timing T w after earthquake: this includes a natural cue (ground shaking). f) Evacuation speeds that depend on demography; we use empirical data for pedestrian moving speeds are available [9, 10]. g) Time of day and time of year: this determines the number and distribution of the population. h) Ambient conditions of evacuation routes C evac : this adjusts the evacuation speeds. i) Most probable preparation time T prep for people to initiate evacuation after they receive tsunami warning: this is estimated based on the consideration of how well the community is prepared. Evacuation Travel Time Evacuation travel times from each population block are computed with input data for 1) walking speeds (mean and standard deviation), 2) slope of the evacuation route, 3) road tortuosity C t, 4) ambient conditions during evacuation, 5) evacuation-route condition considering possible obstacles and damage along the route due to the preceding earthquake (e.g. bridge failure). Wood and Schmidtlein [5] used the walking speeds of hikers described by Tobler [11], which is a function of the ground slope. The average walking speed u ave in m/s and its standard deviation σ walk for each population block can be written as: u ave = 1ˆf n u i f i and σ walk = i 1 ˆf n (u i u ) 2 f i (1) i where u i = 1.19C evac u 0 i e 3.5 θ , u i is a base walking speed on a flat ground for the i-th demographic group, θ is the ground slope, C evac is the adjusting factor for ambient conditions (for example, consideration for snowing night time), f i is the population of the i-th demographic group, ˆf is the total population, and n is the number of demographic groups considered. In order to include potentially adverse conditions in the evacuation routes that might have been caused by the preceding earthquake, we add some penalty distance L obst to the evacuation route C t L in which L is the distance between the centroid of the initial population block and the nearest maximum inundation location X on the road. Evacuation Travel Time T travel can then be calculated for the average evacuation walking speed for each population block: ( L obst ) u ave (2) T travel = C t L + The corresponding error bar is computed as the standard deviation σ walk. To distinguish fatality from injury, the foregoing calculations are repeated to obtain the Evacuation Travel Time for fatality T* travel based on the distance L* that is the distance between the centroid of the initial population block and the nearest location X* on the road along the maximum inundation depth of 2.0 m. Here we assume that 99% of people who remain in the area with the inundation depth greater than 2.0 m would be killed and the injury rate decreases linearly to nil toward the maximum inundation location X.

6 Casualty Estimates Population in each block depends on time of day and season. Casualty also depends on the vulnerability of people: i.e. age and gender [12, 13, 14, 15, 16, 17, 18]. This factor is included through evacuation walking speeds u i. Drowning criteria based on physiology and tsunami dynamics (force balance) (e.g. [18]) are not considered in the present methodology. As discussed earlier, strength of tsunamis (e.g. measured by tsunami runup height) is not a good indicator for predicting casualty rates as indicated in Fig. 1. The important factors are prior knowledge and effective notification. Consequently, temporal inundation information is needed for estimating casualties. The temporal parameters used for our methodology are 1) tsunami arrival time T 0, 2) time of maximum runup T max, 3) tsunami warning timing T w, 4) its effectiveness T prep that represents the time for people to evacuate after tsunami warning, and 5) evacuee travel times T travel and T* travel for injury and fatality estimates, respectively. We first determine the critical time T crit, which represents the time difference between the evacuation time and the available time to evacuate: T crit = T max T w T crit = T max T 0 ( ) when warning before tsunami arrival: T 0 > T w ( ) no warning or warning after tsunami arrival: T 0 < T w ( ) T prep + T travel ( ) T prep + T travel (3) Note that for the latter case, tsunami arrival at the shore is the evacuation cue when tsunami warning is not issued or issued after its arrival. Consider the evacuation time is the median time for a given evacuee population; then, more than half of the population would travel beyond the inundation zone and thus unharmed when the critical time T crit > 0. When T crit < 0, less than half would be unharmed, and when T crit = 0, then it is a 50/50 situation. This is the basis to estimate casualty in our methodology. It is important to recognize that when people receive tsunami warnings (either official warnings or natural cues), not everyone starts to evacuate at once, due to various personal decision making processes. The timing to initiate evacuation is the primary reason why the evacuee pack spreads out from the initial population block. Assuming evacuees population spread is skewed and is kept in the positive time (t > 0), we model the evacuees initial distribution to be lognormal. The choice of lognormal distribution is merely for convenience to form a skewed and smooth distribution function for t > 0. With this caveat, the lognormal probability density function P(t) and the cumulative distribution function D(t) in terms of time t are, respectively: P(t) = 1 s 2π t Exp ( (lnt M )2 2s 2 ) ; D(t) = 1 2 ( ) 1+ erf (lnt M ) s 2 (4) where erf ( ) is the error function, and the parameters s and M are related to the mean µ, the variance σ 2, and the mode of the variable t:

7 µ = Exp( M + s 2 2); σ 2 = Exp( s 2 + 2M ) ( Exp( s ) 2 1); mode = Exp( M s 2 ); median = Exp( M ) (5) In our methodology, we set the evacuation preparation time T prep at the mode of the lognormal distribution, which means that the parameter T prep represent the most probable time for people to initiate evacuation. To determine the necessary variables M and s, we need to identify one more parameter; that is σ. We assume that the spread is related with the warning effectiveness and preparation time T prep. For the present methodology, we set σ = 0.5 T prep which yields a reasonable spread of the lognormal distribution as demonstrated in Fig. 2. Figure 2 shows the resulting probability density function for the time to initiate evacuation with various values of the warning effectiveness and preparation time T prep for both typical local-tsunami and distanttsunami cases. The resulting distributions appear realistic, but can be fine-tuned once better (perhaps empirical) information is obtained. Also note that each distribution function in the figure represents the spread due to response to the warning only: effects of the traveling process are not included, but are considered next. Figure 2. Probability density functions of the population ratio for lognormal distribution with the different values of warning effectiveness and preparation time T prep. Left) for a local tsunami event: tsunami arrival time T 0 = 25 min., time of maximum inundation T max = 30 min., and tsunami warning time T w = 0 (the same time as the earthquake), and T prep = 5, 15, and 25 min. Right) for a typical distant tsunami event: T 0 = 250 min., T max = 255 min., T w = 70 min. and T prep = 36, 108, and 180 min. Once the people begin evacuating towards a safe haven, they further disperse because of difference in walking speeds due primarily to demographic factors. Recall that, in the process of calculating the evacuation travel time T travel, we obtained the mean walking speed u ave, and its standard deviation σ walk. The standard deviation in evacuation speed is converted to standard deviation in time: i.e. σ walk T travel u ave. This standard deviation in time is used to estimate the continuing spread of evacuees during the travel process, when T crit > 0. When T crit 0, we use the standard deviation that occurred during available evacuation time (T max T w ) T prep, instead of T travel. The spread of evacuees due to the difference in walking speed is modeled as the uniform distribution function W (t) with the foregoing standard deviation in time. The combined effect of population spread due to people s response to the warning and their walking speeds can be calculated by the following convolution:

8 F (t ') = P(τ )W (t ' τ )dτ (6) 0 where P(τ) is the lognormal distribution function presented in Eq. 4. The cumulative distribution function of the population can be found: t C (t) = F (t ') dt ' (7) 0 where t represents the time to initiate evacuation, but the distribution is modified with the evacuation process. In other words, t + T travel represents the time after the tsunami warning T w as displayed in the first figure in Fig. 3. Figure 3 also exhibits the corresponding cumulative lognormal distribution function (black line) that resulted from people s response to the warning, and the final distribution function (red line) that includes the effect of different evacuation speeds based on demographic factors. It is important to recall that the preparation time T prep that represents the level of tsunami awareness is used to match the mode of the probability distribution function for the initial response to the warning, i.e. the most probable time for the people to initiate evacuation. Once we obtained the cumulative distribution function C(t), the median value of time T med is determined: C(T med ) = 0.5. The survival rate R survive is the value of the cumulative distribution at t = T med + T crit. And, the casualty rate is R casualty = 1.0 R survive. Figure 3. (Left) Probability density function of the population ratio from the time of the tsunami warning and (Right) the corresponding cumulative distribution function with the travel time being subtracted: the black lines show the distribution for people s response to the tsunami warning, and the red lines show the final distribution including the effect of different walking speeds during their evacuation. The following parameters are used for this example: T prep = 10 min.; T 0 = 25 min.; T max = 30 min.; T w = 0; T travel = 18 min.; u ave = 1.36 m/sec.; σ walk = 0.22 m/sec. The number of casualties consists of the numbers of injuries and fatalities. To distinguish a fatality from an injury, we set a criterion in terms of the inundation depth: we assume that 99% of people would be killed if they were caught in a depth of more than 2.0 m. With the evacuation travel time for fatality T* travel, the foregoing calculations are repeated to obtain the fatality rate R fatality. Here we assume the injury rate decreases linearly from 99% to nil from the point of 2 m inundation depth toward the maximum inundation X. This logic is illustrated in Fig. 4.

9 Total number of casualties for a given population block j can then be calculated by: N j R casualty, where N j is the number of people in the population block j. Then, the number of fatalities NF j and the number of injuries NI j for the population block j can be calculated, repectively by NF j = N j (0.99 R fatality + ½ (R casualty 0.99 R fatality )) (8) NI j = ½ N j (R casualty 0.99 R fatality ) = N j R casualty NF j (9) Total numbers of fatalities and injuries for the community is NF j and NI j, respectively. j j Figure 4. A sketch illustrates the logic to determine fatality and injury. Example Figure 3 (right) shows the cumulative distribution function of the example case with the condition of preparation time T prep = 10 min; tsunami arrival time T 0 = 25 min; time at maximum inundation T max = 30 min; tsunami warning time T w = 0 (essentially immediately upon occurrence of the earthquake); evacuee travel time T travel = 18 min; the mean walking speed, 1.36 m/sec, and the standard deviation in walking speed, 0.22 m/sec. The critical time T crit in Eq. 3 is: T crit = ( T max T w ) ( T prep T travel ) = (30 0) (10 +18) = 2min. and the median value of time T med = 11.9 min can be found at C (T med ) = 50% in Fig. 3 (right). Now, Fig. 3 (right) yields a cumulative distribution of 64.2% at the time 13.9 min, which is the median time, 11.9 min, plus the critical time T crit = 2 min. Consequently the resulting casualty rate is = 35.8%. If we assume the evacuation travel time T* travel to an inundation depth of 2.0 m was 17 min instead of 18 min, leading the critical time T* crit = 3 min; consequently, C (t) at time = = 14.9 min is 70.6%. Therefore the probability of a 99% fatality rate would be 29.4%. For a given population block with say 193 people, Eqn. 8 yields the estimated numbers of fatalities and injuries are respectively:

10 (193) {0.99 (0.294) + ½ ( (0.294))} = 56 people dead, and (193) (0.358) (56) = 13 people injured. Conclusions We proposed herein a methodology for estimating the number of tsunami casualties (fatalities and injuries) for a given coastal community and a given tsunami scenario. It was found from the historical data that tsunami strength represented by tsunami runup heights is not the controlling parameter to determine the casualty rate. More important factors are the level of education and the effectiveness of warning. Therefore, the developed methodology is designed to allow the users to make their own evaluation and judgment calls to characterize the community preparedness and human behaviors. For a given scenario tsunami event, the proposed methodology requires the tsunami arrival time T 0, the time of maximum runup T max, and the tsunami warning timing T w. It is emphasized that, unlike agent-based modeling, no detailed time histories of inundation depths and flow velocities are required for the methodology. Human response to warnings is characterized by the preparation time T prep that represents the time for people to evacuate after the tsunami warning. The methodology also incorporates many other relevant factors that influence the casualty rate: e.g. obstruction and ambient conditions in the evacuation routes, demographic situations, etc. With consideration of many relevant factors, the developed methodology is rational and based on proper logics. The methodology is considered as a simplified version of agent-based modeling, and can be used as a tool to estimate casualties for coastal communities under given tsunami scenarios without performing numerical simulations for detailed tsunami inundation. Acknowledgments This work was supported as part of the development of MH HAZUS by FEMA through Atkins North America. Critical reviews by the oversight committee and the methodology development team are acknowledged. References 1. USAID, Tsunami Relief. Bureau for Legislative and Public Affairs, 29 pp. 2. National Police Agency, Suppasri, A., Koshimura, S., Imai, K., Mas, E., Gokon, H., Muhari, A., and Imamura, F Damage characteristics and field survey of the 2011 Great East Japan Tsunami in Miyagi Prefecture. Costal Engineering Journal, 54(1), DOI: /S Wood, N.J., Schmidtlein, M.C Anisotropic path modeling to assess pedestrian-evacuation potential from Cascadia-related tsunamis in the US Pacific Northwest. Natural Hazards, DOI /s Katada, T., Kuwasawa, N., Yeh, H., and Pancake, C Integrated simulation of tsunami hazards, The 8th National Conference on Earthquake Engineering, San Francisco.

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