# New Exploratory Tools for Extremal Dependence: Chi Networks and Annual Extremal Networks

## TL;DR

This paper introduces novel network-based tools, the Chi network and annual extremal network, for analyzing extremal dependence in environmental data, with applications to hurricane-related precipitation extremes.

## Contribution

It develops new estimators and bias correction methods for extremal dependence networks, and applies them to real hurricane data to reveal spatial and temporal extremal dependence patterns.

## Key findings

- Long-distance extremal dependence exists in precipitation extremes.
- Dependence strength varies with regional meteorological conditions.
- The methods effectively capture temporal and spatial extremal dependence.

## Abstract

Understanding dependence structure among extreme values plays an important role in risk assessment in environmental studies. In this work we propose the $\chi$ network and the annual extremal network for exploring the extremal dependence structure of environmental processes. A $\chi$ network is constructed by connecting pairs whose estimated upper tail dependence coefficient, $\hat \chi$, exceeds a prescribed threshold. We develop an initial $\chi$ network estimator and we use a spatial block bootstrap to assess both the bias and variance of our estimator. We then develop a method to correct the bias of the initial estimator by incorporating the spatial structure in $\chi$. In addition to the $\chi$ network, which assesses spatial extremal dependence over an extended period of time, we further introduce an annual extremal network to explore the year-to-year temporal variation of extremal connections. We illustrate the $\chi$ and the annual extremal networks by analyzing the hurricane season maximum precipitation at the US Gulf Coast and surrounding area. Analysis suggests there exists long distance extremal dependence for precipitation extremes in the study region and the strength of the extremal dependence may depend on some regional scale meteorological conditions, for example, sea surface temperature.