This thesis examines the indirect impact of natural hazards on infrastructure networks. It addresses several key themes and issues for hazard assessment, network modelling and risk assessment using the case study of landslides impacting the national road network in Scotland, United Kingdom. The research follows four distinct stages. First, a landslide susceptibility model is developed using a database of landslide occurrences, spatial data sets and logistic regression. The model outputs indicate the terrain characteristics that are associated with increased landslide potential, including critical slope angles and south westerly aspects associated with increased rates of solar irradiance and precipitation. The results identify the hillslopes and road segments that are most prone to disruption by landslides and these indicate that 40 % (1,700 / 4,300 km) of Scotland s motorways and arterial roads (i.e. strategic road network) are susceptible to landslides and this is above previous assessments. Second, a novel user-equilibrium traffic model is developed using UK Census origin-destination tables. The traffic model calculates the additional travel time and cost (i.e. indirect impacts) caused by network disruptions due to landslide events. The model is applied to calculate the impact of historic scenarios and for sets of plausible landslide events generated using the landslide susceptibility model. Impact assessments for historic scenarios are 29 to 83 % greater than previous, including £1.2 million of indirect impacts over 15 days of disruption at the A83 Rest and Be Thankful landslide October 2007. The model results indicate that the average impact of landslides is £64 k per day of disruption, and up to £130 k per day on the most critical road segments in Scotland. In addition to identifying critical road segments with both high impact and high susceptibility to landslides, the study indicates that the impact of landslides is concentrated away from urban centres to the central and north-west regions of Scotland that are heavily reliant on road and haulage-based industries such as seasonal tourism, agriculture and craft distilling. The third research element is the development of landslide initiation thresholds using weather radar data. The thresholds classify the rainfall conditions that are most commonly associated with landslide occurrence in Scotland, improving knowledge of the physical initiation processes and their likelihood. The thresholds are developed using a novel optimal-point threshold selection technique, high resolution radar and new rain variables that provide spatio-temporally normalised thresholds. The thresholds highlight the role of the 12-day antecedent hydrological condition of soils as a precursory factor in controlling the rain conditions that trigger landslides. The new results also support the observation that landslides occur more frequently in the UK during the early autumn and winter seasons when sequences or clustering of multiple cyclonic-storm systems is common in periods lasting 5 to 15 days. Fourth, the three previous elements are combined to evaluate the landslide hazard of the strategic road segments and a prototype risk assessment model is produced - a catastrophe model. The catastrophe model calculates the annual average loss and aggregated exceedance probability of losses due to the indirect impact of landslides in Scotland. Beyond application to cost-benefit analyses for landslide mitigation efforts, the catastrophe model framework is applicable to the study of other natural hazards (e.g. flooding), combinations of hazards, and other infrastructure networks.

Title: Actuarial and Exposure-based Models for Hail Peril Author: Bc. Matúš Drobuliak Department: Department of Probability and Mathematical Statistics Supervisor: RNDr. Michal Pešta, Ph.D., Department of Probability and Mathe- matical Statistics Abstract: This thesis covers an introduction to catastrophe modelling and focuses on statistical methods for extreme events. This includes methods of estimating parameters of claim distribution with a focus on probability weighted moments estimation technique. Furthermore, times series modelling, skew t-distribution, and two model clustering techniques are examined as well. This is later utilised in the practical application part of this thesis, which uses real data provided by an insurance company operating in the Czech Republic. Probability distribution fitting of large claims caused by hailstorms and Monte Carlo simulation of future losses are demonstrated later. Keywords: Catastrophe modelling, Hail peril, Probability weighted moments, Extreme events, ARMA-GARCH, Monte Carlo simulation iii

The research attempts to resolve which method of estimation is the most consistent for the parameters of the earthquake model, and how these different methods of estimation, as well as other changes, in the earthquake model parameters affect the damage estimates for a specific area. The research also investigates different methods of parameter estimation in the context of the log-linear relationship characterised by the Gutenberg-Richter relation. Traditional methods are compared to those methods that take uncertainty in the underlying data into account. Alternative methods based on Bayesian statistics are investigated briefly. The efficiency of the feasible methods is investigated by comparing the results for a large number of synthetic earthquake catalogues for which the parameters are known and errors have been incorporated into each observation. In the second part of the study, the effects of changes in key parameters of the earthquake model on damage estimates are investigated. This includes an investigation of the different methods of estimation and their effect on the damage estimates. It is found that parameter estimates are affected by observation errors. If errors are not included in the method of estimation, the estimate is subject to bias. The nature of the errors determines the level of bias. It is concluded that uncertainty in the data used in earthquake parameter estimates is largely a function of the quality of the data that is available. The inaccuracy of parameter estimates depends on the nature of the errors that are present in the data. In turn, the nature of the errors in an earthquake catalogue depends on the method of compilation of the catalogue and can vary from being negligible, for single source catalogues for an area with a sophisticated seismograph network, to fairly impactful, for historical earthquake catalogues that predate seismograph networks. Probabilistic seismic risk assessment is used as a catastrophe modelling tool to circumvent the problem of scarce loss data in areas of low seismicity and is applied in this study for the greater Cape Town region in South Africa. The results of the risk assessment demonstrate that seemingly small changes in underlying earthquake parameters as a result of the incorporation of errors can lead to significant changes in loss estimates for buildings in an area of low seismicity. / Dissertation (MSc)--University of Pretoria, 2014. / Insurance and Actuarial Science / MSc / Unrestricted