Chapter 24 - Univariate, multivariate L-moments and copula functions for drought analysis

Abstract

Humans have faced many natural disasters since ancient times and have seen the bad effects on their lives. These natural disasters include prolonged droughts and severe floods. Drought and flood are some of the most important natural disasters in the world, which are likely to occur due to geographical conditions in all parts of the world. These natural hazards affect vulnerable areas. Drought, for example, has a gradual effect and occurs over a relatively long time. Therefore, drought can be considered as a climatic phenomenon that harms both the natural environment and human life. Drought problems must be overcome by creating preparedness management plans. Understanding the characteristics of drought is an important issue in the optimal management of drought management programs. On the other hand, defining drought based on one variable alone is not sufficient to assess and manage drought risks. Therefore, recent studies on drought have used multivariate methods. The construction of multivariate indicators has been considered by many researchers in this field. Although the univariate L-moment (L-moment) method has strong advantages for modeling different distributions, such as some of the distributions used in hydrology, this method could be problematic. Multivariate statistical analysis relies heavily on second and higher order instantaneous hypotheses. Due to the increasing interest in bivariate heavy-tailed distribution, the description of scattering, deviation, skewness, and kurtosis is desirable only in first-order moment assumptions (Selfring and Xiao, 2007). Therefore, the purpose of this study is to investigate the drought in the different parts of the world using multivariate indicators. Studies show that the study of drought using the L-moment method and the study of meteorological, agricultural, and hydrological droughts simultaneously in a region provides more acceptable results of drought.