Copula-based multivariate analysis of hydro-meteorological drought

Abstract

Droughts have a wide range of adverse impacts on the environment, society, and economy ranging from regional to national levels. Multivariate analysis of drought characteristics (i.e., drought duration, severity, peak, etc.) is necessary to get a picture of the actual drought situation in a region as these characteristics are interrelated. However, such studies are limited. Therefore, the current study developed a framework to investigate the meteorological and hydrological droughts based on a multivariate analysis of drought characteristics in the Pennar river basin of India which is located in a semi-arid region where agricultural activity is dominant. Long-term observations of precipitation, temperature, and streamflow for the period of 1980-2015 were used to calculate Standardized Precipitation Evapotranspiration Index (SPEI) and Streamflow Drought Index (SDI), at a 3-month timescale. Based on these indices, three drought characteristics (i.e., drought duration, severity, and peak) were abstracted using the Run Theory. The best-fit marginal distribution was determined for each of the drought variables and those best-fit marginal distributions were used to get the bivariate joint probability distribution, i.e., the copula function. The Copula function was used to figure out the joint probability distribution of multiple variables. Based on the best-fit copula function, joint multivariate distributions have been established and the joint probabilities and the joint return period have been estimated. Results revealed that, out of the nine copula functions, for the overall region of the river basin, for meteorological drought, Frank Copula is found to be the best-fit copula function for the joint risk of drought duration and severity, whereas Survival Clayton copula is found to be the best-fit copula for the combination of both drought duration and peak as well as drought severity and peak. The probability of occurrence of a drought event with specified characteristics of duration, severity, and peak was obtained for the study area based on Copula-based joint probability analysis. The joint return period of a drought event with characteristics greater than the 25 th percentile of the same for the study area is varying from 1 to 2 years whereas it varies from 1 year to 45 years for the 50 th percentile. This analysis will provide important information required for water management and planning in a region to mitigate droughts.

Vine Copula-Based Multivariate Distribution of Rainfall Intensity, Wind Speed, and Wind Direction for Optimizing Qatari Meteorological Stations

“…In other fields of hydrology, copula functions have been applied. For example, Shaw and Chitra [24] examined droughts using Copula functions. Vernieuwe et al [20] and Bi et al [22] introduced a Vine Copula to model the dependence structure of the governing variables.…”

Meteorological and Hydrological Drought Risks under Future Climate and Land-Use-Change Scenarios in the Yellow River Basin

“…Chang et al [26] assessed the multivariate integrated drought risk in the Wei River Basin through the joint probability distribution of drought duration and severity based on Archimedean copulas. Shaw and Chithra [27] developed a copula-based framework to investigate the meteorological and hydrological droughts using a multivariate analysis of drought characteristics in the Pennar River basin (a semi-arid region) of India. However, existing drought risk assessments using copula functions primarily focus on historical frequencies rather than future projections, leaving a gap in copula-based drought modeling under climate and land-use-change scenarios for the YRB.…”