Estimation of tail dependence coefficient in rainfall accumulation fields

Amir Aghakouchak,Grzegorz Ciach,Emad Habib

doi:10.1016/j.advwatres.2010.07.003

Amir Aghakouchak, Grzegorz Ciach + Show 1 more

Open Access

https://doi.org/10.1016/j.advwatres.2010.07.003

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Abstract

Extreme rainfall events are of particular importance due to their severe impacts on the economy, the environment and the society. Characterization and quantification of extremes and their spatial dependence structure may lead to a better understanding of extreme events. An important concept in statistical modeling is the tail dependence coefficient (TDC) that describes the degree of association between concurrent rainfall extremes at different locations. Accurate knowledge of the spatial characteristics of the TDC can help improve on the existing models of the occurrence probability of extreme storms. In this study, efficient estimation of the TDC in rainfall is investigated using a dense network of rain gauges located in south Louisiana, USA. The inter-gauge distances in this network range from about 1 km to 9 km. Four different nonparametric TDC estimators are implemented on samples of the rain gauge data and their advantages and disadvantages are discussed. Three averaging time-scales are considered: 1 h, 2 h and 3 h. The results indicate that a significant tail dependency may exist that cannot be ignored for realistic modeling of multivariate rainfall fields. Presence of a strong dependence among extremes contradicts with the assumption of joint normality, commonly used in hydrologic applications.

Highlights

Extreme precipitation events are of particular importance due to their impacts on economy, environment and human life
Considering different extreme value thresholds (75, 90 and 95 percentile) and time durations, the figures show that λ(3) offers the least values of the estimated tail dependence coefficient (TDC)
A comparison between the left, middle and right columns of panels (Fig. 3(a) to (i)) reveals that the TDCs drop down fairly for all the other estimators as the threshold increases. This implies that the effect of sample size on the estimated TDC is almost similar for the methods used in this study

Summary

Introduction

Extreme precipitation events are of particular importance due to their impacts on economy, environment and human life. Characterization and quantification of extremes and their spatial dependence structure may lead to better estimates of probability occurrence of rare events. Most commonly used measures of dependence such as the Pearson linear correlation and Spearman [39] correlation are not able to correctly describe the dependence of extremes [25]. While the Spearman correlation always exists, the Pearson linear correlation may not exist for random variables above a certain extreme threshold [9]. Most measures of dependence are based on the association of the entire distributions of multiple variables. The degree of association (dependence) between extreme values may be significantly different [11] than that of the mid-range values (e.g., the dependence of extremes may be stronger than the mid-range values or vice versa)

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