Tsunami evacuation risk assessment and probabilistic sensitivity analysis using augmented sample-based approach

Highlights

• Uses a novel agent-based tsunami evacuation model to simulate tsunami evacuation.

• Explicitly quantifies various uncertainties in the evacuation process.

• Uses an augmented sample-based approach for efficient analysis.

• Only needs one set of samples to calculate sensitivity for all uncertain parameters.

• Provides important insights on tsunamic evacuation and effective risk mitigation.

Abstract

Tsunami evacuation is an effective way to save lives from the near-field earthquake-induced tsunami. To accurately assess tsunami evacuation risk, various uncertainties in evacuation need to be considered. For risk mitigation, it is also important to identify critical parameters (or risk factors) that contribute more to the evacuation risk to guide more effective tsunami evacuation. Probabilistic sensitivity analysis can be used for the latter. However, both risk assessment and sensitivity analysis require a large number of model evaluations and entail significant computational challenges, especially for the expensive evacuation model. This paper proposes an efficient augmented sample-based approach to address the above challenges. It only requires one set of samples/simulations (hence the high efficiency) to estimate the evacuation risk and calculate the sensitivity measures for all uncertain parameters. The approach is applied to estimate the tsunami evacuation risk for Seaside, Oregon, where a novel agent-based tsunami evacuation model is used to simulate the evacuation process more realistically. Various uncertainties in the evacuation process are explicitly quantified by properly selected probability distribution models. Besides the evacuation risk, critical risk factors are identified using probabilistic sensitivity analysis. The results provide important insights on tsunami evacuation and critical information for guiding effective evacuation risk mitigation.

Introduction

An earthquake-induced tsunami can cause huge economic and life losses [1,2]. Evacuation to safety zones is regarded as an effective way to survive a tsunami [3,4]. Accurate tsunami evacuation risk assessment and identification of critical factors that impact evacuation can provide important information for guiding the selection of optimal evacuation risk mitigation strategies [3,[5], [6], [7]].

To accurately assess the evacuation risk, various uncertainties associated with the evacuation need to be considered. There are significant sources of uncertainties in the evacuation process, related to the multiple hazards (i.e., cascading hazards of earthquake and tsunami), the seismic damages to the built infrastructure environment (e.g., transportation/road network), the population size, and spatial distribution, and the evacuation behaviors of the population (e.g., decision to evacuate or not, when to evacuate, how to evacuate (on foot or by car), evacuation speed variability for different age groups). To accurately assess the evacuation risk, these uncertainties need to be properly quantified. However, existing research typically neglects many (if not all) of these uncertainties. For example, seismic damage to the links (i.e., bridges and roads) of the transportation network could cause a significant reduction in traffic capacity and hence delay the evacuation [8,9]. However, seismic damage of links and the associated uncertainties are typically neglected or considered in a simplified way (e.g., by removing the damaged links from the network, essentially assuming complete damage all the time) [6,9,10].

To quantify the uncertainties, probability distribution models can be used. These distribution models typically have some hyperparameters or distribution parameters (e.g., mean and standard deviation of the Gaussian distribution). Many times, we are interested in the risk conditional on different values of the distribution parameters, i.e., under different distribution models. Assessment of such conditional evacuation risk can provide important information for evacuation risk mitigation and evacuation planning. In such context, direct (i.e., repeated) use of stochastic simulation techniques such as Monte Carlo Simulation (MCS) [11] to estimate the risk conditional on different values of the distribution parameters would entail huge computational challenges, especially for the expensive evacuation model.

To reduce the evacuation risk (e.g., casualty rate) effectively, critical factors in evacuation need to be identified, based on which optimal mitigation strategies can be selected to effectively reduce the evacuation risk. Probabilistic sensitivity analysis is commonly used to identify the importance of different parameters [[12], [13], [14], [15], [16], [17]]. However, research on tsunami evacuation sensitivity typically uses simplified parametric study rather than conducting the full probabilistic sensitivity analysis (i.e., including the uncertainty of the model parameters) [6,9,18]. General stochastic simulation techniques, e.g., MCS, can be used to perform probabilistic sensitivity analysis. However, typically a large number of simulations are required, which entails significant computational challenges, especially when expensive agent-based modeling (ABM) is used to simulate the evacuation [19,20]. The sample-based approach in Refs. [15,16] can help alleviate the above computational challenges. However, similar to the evaluation of conditional risk, it will also need to be repeated when performing probabilistic sensitivity analysis conditional on different values of the distribution parameter.

To address the above computational challenges, this paper extends the augmented sample-based approach in Ref. [21] (proposed for estimating risk sensitivity with respect to epistemic uncertainty of distribution parameter) to efficiently perform tsunami evacuation risk assessment and probabilistic sensitivity analysis conditional on different values of the distribution parameter. It relies on generating one set of samples from a joint auxiliary distribution in the augmented space of both model parameters and distribution parameters. On one hand, unlike in Ref. [21] where the distribution parameter is uncertain, here the distribution parameters of interest (which are not uncertain) are artificially treated as uncertain with some distributions. This extension enables the use of the augmented sample-based approach for efficient tsunami evacuation risk assessment and probabilistic sensitivity analysis under different values of the distribution parameters. On the other hand, unlike in Ref. [21] where only marginal auxiliary distribution for the distribution parameter needs to be approximated, here the marginal auxiliary distribution for the model parameter conditional on different values of the distribution parameters of interest is needed for probabilistic sensitivity analysis. Instead of directly generating conditional samples, the conditional distribution is efficiently estimated using the definition of conditional distribution and the existing set of auxiliary joint samples. Bayes theorem is used to address the estimation of conditional distribution for discrete model parameters. With the above extensions, the augmented sample-based approach has great efficiency and provides the conditional risk estimation and conditional sensitivity information for all uncertain model parameters simultaneously. To simulate the evacuation process, the novel agent-based tsunami evacuation model introduced in Ref. [22] is used to simulate the evacuation more realistically, which includes features such as multi-modal evacuation (i.e., evacuation on foot and by car), pedestrian–vehicle interaction, walking speed variability, and speed adjustment for pedestrians and cars. Various uncertainties are considered for more accurate risk assessment. The approach is applied to tsunami evacuation risk assessment and probabilistic sensitivity analysis of the coastal community of Seaside, Oregon. The established risk and sensitivity information can be used to guide the selection of mitigation strategies (e.g., retrofit the critical links, or change people's evacuation behavior) to reduce the tsunami evacuation risk most effectively.

The remainder of this paper is organized as follows. Section 2 introduces the framework for quantification of tsunami evacuation risk. Section 3 introduces the adopted probabilistic sensitivity measure. Section 4 presents the main idea of the augmented sample-based approach for efficient conditional risk assessment and conditional probabilistic sensitivity analysis. Section 5 describes the agent-based tsunami evacuation model. Section 6 applies the augmented sample-based approach to an example coastal community to evaluate its tsunami evacuation risk and identify the critical risk factors. Section 7 summarizes the research findings.