New Approaches to At-site and Regional Frequency Analysis of Hydrologic Extremes in Peaks Over Threshold Framework

Abstract

Frequency analysis procedures are widely used to quantify the risk associated with floods that have devastating consequences worldwide. Conventionally, the frequency analysis is performed based on the annual maximum series (AMS) of peak flows extracted from the available streamflow records. Peaks-over-threshold or Partial duration series (PDS) framework is deemed more efficient than AMS in depicting information on extremes. Despite its advantages, the use of PDS is less prevalent than AMS. It is due to the lack of a universally established systematic approach to select an appropriate threshold for PDS extraction. Various issues affect the performance of different methods available for threshold selection. A novel Mahalanobis distance-based automatic threshold selection method is proposed to address those issues, and its potential is demonstrated over four automatic threshold selection methods. Another issue in flood risk assessment at target locations is sparsity or lack of data. In such situations, practitioners opt for regional frequency analysis (RFA) approaches that involve regionalization (locating groups/regions comprising resembling watersheds) and pooling of flood-related information from outlets of the watersheds to estimate desired flood quantile(s) at the target sites. Most RFA approaches are focused on using AMS rather than PDS. This thesis addresses regionalization-related issues and focuses on leveraging the advantages of using PDS in RFA. Regionalization approaches are many, and their choice is ambiguous as none is established to be universally superior. They differ in their underlying assumptions and strategies, and thus yield regions that vary in composition. A new entropy-based fuzzy ensemble clustering approach is proposed to address the uncertainty in regionalization. It forms effective fuzzy meta-regions by ameliorating information from regions derived using different procedures. Error in flood quantile estimates at ungauged sites based on those meta-regions was the least in Monte-Carlo simulation (MCS) experiments and case studies on river basins in peninsular India. One could avert the risk of picking an unsuitable regionalization method by opting for ensemble clustering.

The index-flood approach and its variants are widely used for the past six decades to perform RFA, though they make several unrealistic assumptions. Consequently, various alternative techniques have been proposed in the literature. However, most of them focus on using AMS, and there is hardly any based on PDS. Against this backdrop, two new RFA techniques based on random forests (RFs), namely generalized Pareto distribution (GPD) based distributional RFs (DRFs) and Multivariate RFs, are proposed for use with PDS. The new DRFs-based technique is shown to outperform two recently proposed techniques and Multivariate RFs through MCS experiments and a case study on the conterminous United States. Investigations were also carried out to identify important/key watershed-related features useful in predicting the scale and shape parameters of GPD. There are no prior attempts in this direction using PDS. Another important fact is that RFA of floods in a multivariate framework is deemed more appropriate, as floods can be better characterized by several correlated variables such as flood peak, volume, duration, and time to peak. However, RFA has received little attention in the multivariate framework. The available literature recommends using a multivariate extension of the index-flood-based approach (considering AMS), even though it has theoretical shortcomings. Against this backdrop, a novel multivariate RFA approach based on the conditional multivariate extreme values model (CEA) is proposed. It facilitates flood risk assessment at sparsely gauged and ungauged locations by predicting the joint distribution of multiple flood-related variables using information pooled from resembling watersheds. The potential of CEA over a recently proposed index-flood-based multivariate RFA approach is demonstrated through MCS experiments and a case study on a flood-prone region of India.