Modeling the Dependence Structure of Hydroclimatic Extremes

Abstract

Analysis of extremes in a complex interacting hydroclimatic system is challenging due to rarity of events, small sample size, poor state of data or missing data, lack of statistical tools for analyzing observed changes and poor understanding of interactions of extremes. This thesis addresses the challenge of lack of statistical tools specifically suited for modeling hydroclimatic extremes. Significant changes are observed in the intensity, frequency, duration, timing and spatial extent of hydroclimatic extremes. Understanding the nature of these changing characteristics is a major challenge for hydroclimatic research community. Recent high impact extremes provide strong evidences for the interconnections of extremes. The boundaries of system are widening with the changes leading to a greater need to consider the dependencies between interacting processes for reliable risk estimates. A contribution of this thesis is to identify statistical procedures for modeling the extremal dependence structure in order to facilitate accurate probabilistic characterization of hydro-meteorological processes. Extreme rainfall is the most common cause of flooding and likelihood of such events is found to increase in recent studies. Large scale natural variability, human induced global warming and local atmospheric warming are important drivers of extreme rainfall. A methodology to investigate the association of daily rainfall extremes with plausible physical drivers is presented in this thesis. Non-stationary extreme value models are used to investigate the association and Copula theory is used to capture the dependence structure of extreme rainfall with the most significant physical driver. A combination of multiple processes can lead to devastating consequences, making the recovery of the system more difficult. Common statistical modeling practices or conceptual frameworks cannot capture the interrelationships of multiple extreme events which mutually enhance each-other. A statistical procedure to investigate the changes in the characteristics of concurrent meteorological droughts and heatwaves is presented in the thesis. Changes in the frequency and spatial extent of concurrent extremes are quantified over India to identify the hotspots which need immediate attention. The complex nature of concurrent extremes requires a new perspective for robust risk assessment. This thesis identifies parametric multivariate extreme value models as a suitable tool to model the dependence structure of concurrent extremes and disentangle their complex interactions. Extremal dependence structure of rainfall deficits, soil moisture deficits and high temperatures is explicitly described through angular densities on the two-dimensional simplex. These models can provide a powerful new perspective for appropriate statistical analysis of dependent hydroclimatic extremes in higher dimensions. Clustering of extreme rainfall in short period of time is responsible for huge economic and environmental losses. Extreme value models have been widely used to model the magnitudes of extreme events; however, little attention is paid to the duration of the extreme events due to challenges in modeling the dependence within the clusters of exceedances. This thesis presents a hierarchical Bayesian model to capture the temporal dependence structure of extreme rainfall spells. Specifically, this model addresses the risk of a flooding situation which arises due to heavy rainfall for a few consecutive days. The work presented in this thesis emphasizes the necessity of capturing the dependence structure of extremes to improve the understanding, modeling and prediction of hydroclimatic extremes.