Non-Stationary Stochastic Modelling of Climate Hazards for Risk and Reliability Assessment

Abstract

This thesis presents methodologies for studying the effects of climate change on natural hazards. The thesis is structured around three key aspects: first, the stochastic modelling of non-stationary hazards; second, the modelling of concrete degradation in a changing climate; and third, the economic risk evaluation associated with these non-stationary hazards.

The initial focus of this thesis is on applying a non-stationary stochastic process to model the increasing frequency and intensity of climate-driven hazards in Canada. The early chapters provide an overview of the effects of climate change in Canada. To understand the trends and projections of various climatic variables, such as temperature, precipitation, and wind speed, recent studies and reports from Environment and Climate Change Canada, along with other relevant literature, are examined and analyses were performed on the model outputs of the Couple Model Inter-comparison Project Phase 6 (CMIP6) data. The overview highlights the growing occurrence and severity of climate hazards, including hurricanes, droughts, wildfires, and heatwaves, as supported by other independent studies. In the light of such analyses, this study demonstrates the inadequacy of traditional stationary models for future predictions and risk assessments, thereby advocating for a shift to non-stationary frameworks.

The thesis provides a robust theoretical foundation for non-stationary hazard modelling using stochastic process models. Traditional extreme value analysis (EVA) typically assumes stationarity. However, this assumption is invalidated by gradual changes in the frequency and intensity of climate-driven hazards. This research proposes methodologies to model climatic hazards using a non-stationary stochastic shock process, specifically the non-homogeneous Poisson process (NHPP), to derive the maximum value distributions over any finite period and not just restricted to annual maxima. These models account for changes in the underlying processes over time, providing a more accurate representation of climate-driven hazards by incorporating time-varying parameters that reflect the dynamic nature of climatic extremes. By integrating stochasticity and temporal variability, these stochastic process models offer a robust framework for predicting the future occurrence and intensity of climate-driven hazards. The proposed methods are demonstrated through the estimation of maximum value distributions for precipitation events using the Coupled Model Inter-comparison Project (CMIP) phase-6 multi-model ensemble data, with an analysis of inter-model variability. Furthermore, the thesis presents a case study on modeling heatwaves to illustrate the application of these models to climatic data, particularly for events where the asymptotic assumptions of extreme value theory do not hold.

Climate change will not only influence the loads and hazards on infrastructure, but it will also exacerbate the degradation processes of structures due to harsher climatic conditions such as higher temperatures and increased humidity. To model these effects on the degradation of concrete bridges, simulations were conducted using physico-chemical concrete degradation processes. Based on the simulation results, non-stationary Markov transition probabilities were estimated for several key locations in Canada under various Shared Socioeconomic Pathway (SSP) scenarios.

The final chapter of the thesis addresses the economic aspects of climate-driven hazards. It includes derivations to estimate various statistics of damage costs, such as the mean, variance, moments, and distribution, resulting from a non-stationary hazard process. The analytical results were derived for several cases, such as considering the loss magnitudes to be identically and non-identically distributed, and whether discounting is applied to the losses or not to address the effect of time in evaluating the net present losses or not. This analysis offers valuable information for policy makers, engineers, and scientists involved in climate adaptation and mitigation efforts.