Joint modelling of drought characteristics derived from historical and synthetic rainfalls: Application of Generalized Linear Models and Copulas

Abstract

Study region Çoruh Basin in Northeastern Turkey. Study focus In recent years, copulas have been widely used to model the joint distribution function of duration and severity series which are the major characteristics of a drought event to be considered in the planning and management of water resources systems. However, as the copula functions are typically fitted to the drought series that are derived from a limited amount of observed data, it may be insufficient to characterize the full range of the analyzed drought characteristics. Therefore, General Linear Models (GLMs) were used to model and simulate rainfall data in this study. The Standard Precipitation Index (SPI) method was used to obtain the drought characteristics from simulated and historical rainfall series. Four Archimedean copulas, namely Ali-Mikhail-Haq, Clayton, Frank and Gumbel-Hougaard, were evaluated to model the joint distribution functions of these characteristics. New hydrological insights for the region The Gumbel-Hougaard copula was found to be the most suitable copula in modelling the joint dependence structure of the drought characteristics at five stations in the basin. The derived Gumbel-Hougaard copulas for each station were employed to obtain joint and conditional return periods of the historical and generated drought characteristics. The drought risks that are estimated based on bivariate return periods for different circumstances can provide useful information in planning, management and in assessing adequacy of the water structures in the basin

Copula-Based Drought Analysis Using Standardized Precipitation Evapotranspiration Index: A Case Study in the Yellow River Basin, China

“…The extensive application of Copula showed that it could better fit multiple characteristic variables and could also be applied in many research fields. Applying Copula to the study of drought characteristics and choosing the best-fitted Copula to identify the drought return period is of great practical significance for promoting the sustainable development of arid regions [31].…”

Application of Copula Functions for Rainfall Interception Modelling

“…Moreover, copula functions have been used several times for rainfall analysis and modelling. Some examples of this include: for rainfall frequency analysis in order to estimate reliable design rainfall (e.g., [32][33][34][35][36][37]), for disaggregation of rainfall data (e.g., [38,39]), to construct intensity-duration-frequency (IDF) curves for different purposes (e.g., [40][41][42]), for rainfall generation and modelling (e.g., [43][44][45]), for drought analyses and characterisation of drought properties (e.g., [46][47][48][49][50][51][52][53][54][55][56][57]), and for other rainfall related analyses (e.g., [58][59][60][61][62][63][64]). However, one should bear in mind that research dealing with copula functions is also very intense in the Statistics Probability category (e.g., more than 250 papers were published in 2017 in this category according to the Web of Science database).…”

Comparison of the temporal distribution pattern of precipitation and the cumulative effect of daily droughts on the local scale in Iran

“…10). The Gumbel copula showed a better fit compared to the other two copula methods (Frank and Gaussian) (Tosunoğlu and Onof 2017;Kiafar et al 2020) based on Kendall's tau-b coefficient and the lowest values of AIC (Akaike information criterion) (Akaike 1974). This figure shows the pattern of transmission of drought characteristics over time at Abali station on monthly (SPI) and annual (CZI) scales.…”