Journal Articles

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    Modelling time-inhomogeneous incomplete records of point processes using variants of hidden Markov models
    (Springer Nature, 2025-04-23) Shahzadi A; Wang T; Parry M; Bebbington M
    Many point processes such as earthquakes or volcanic eruptions have incomplete records with the degree of incompleteness varying over time. For these point processes, the number of missing events between each pair of consecutively observed events can be a random variable that may depend on time, effecting the estimation of parameters or hazard. Such incomplete point processes can be modelled by compound renewal processes where the sum of renewal processes is a random variable because of random variable number of missing events. We propose shifted compound Poisson-Gamma and time-dependent shifted compound Poisson-Gamma renewal processes. Since the number of missing events can be regarded as an unobserved process, the proposed renewal processes are introduced to use in the framework of different types of homogeneous and inhomogeneous hidden Markov models to model the time-dependent variable number of missing events between each pair of consecutively observed events of incomplete point processes. Simulation experiments are employed to check the performance of proposed renewal processes with hidden Markov models. We apply the proposed models to the large magnitude explosive volcanic eruptions database to analyze the time-dependent incompleteness and demonstrate how we estimate the completeness of the record and the future hazard rate.
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    Modelling spatial population exposure and evacuation clearance time for the Auckland Volcanic Field, New Zealand
    (Elsevier BV, 2021-08) Wild AJ; Bebbington MS; Lindsay JM; Charlton DH
    Auckland, New Zealand's largest city (population of ~1.6 million), is situated atop the monogenetic Auckland Volcanic Field (AVF). As in many places faced with volcanic activity, evacuation is seen as the best risk mitigation strategy for preserving lives in the event of volcanic unrest and/or an eruption. However, planning for an evacuation can be challenging. In particular, the uncertainty in vent location resulting from the monogenetic nature of the field makes identifying neighbourhoods to be evacuated impractical until well into the pre-eruption unrest period. This study uses spatial analysis methods to assess exposure for both population and private transport ownership as well as to identify those areas requiring public transport support for an evacuation. These data were overlaid on a range of possible vent locations across the AVF using a 500 × 500 m grid. At each possible vent location, a 5 km evacuation zone is modelled, following the official contingency plan for evacuation in a future AVF event. In order to simulate vent location uncertainty leading up to a future eruption, a range of buffer distances were applied around the modelled vent locations. The exposure data derived were then used to model evacuation clearance time, which considered four phases: 1) the time taken to decide to call an evacuation; 2) the public notification time; 3) the evacuee's time to prepare; and 4) evacuee's travel time to beyond the evacuation zone. The length of time involved in phases 1 to 3 are all independent of the vent location; our analysis found these phases could be completed within 36 h, with over 80% confidence. Travel times to beyond the evacuation zone were modelled using the exposure analysis for population and private transport ownership combined with road network data and vehicle carrying capacity. This revealed travel times for this phase ranging from less than 1 up to 11 h, depending on traffic congestion, when considering no vent uncertainty. By combining the times modelled for all four phases, we found that when there is high certainty in the vent location, the median total evacuation clearance time with no congestion is approximately 37 h. However, include a 10 km vent uncertainty buffer into the model, the evacuation clearance time can increase to between 38 and 55 h, dependent on traffic congestion. A vent in the densely populated inner Auckland and CBD area would result in the greatest population required to evacuate, and also the greatest need for public transport support given the low vehicle ownership in this area. Our results can be used to inform emergency management decision making, and the model can be adapted for other regions as well as for other hazards.