Modeling multivariate standardized drought index based on the drought information from precipitation and runoff: a case study of Hare watershed of Southern Ethiopian Rift Valley Basin

Abstract

Drought is below-normal availability of rainfall, runoff, and or soil moisture for a prolonged period in a given region. Modeling drought index using multiple variables is important for future hydrological drought monitoring and sustainable water resource management. This study aimed to model multivariate standardized drought index (MSDI) based on the drought information from precipitation and runoff. Long year (1980–2014) monthly observed precipitation and runoff data were used to analyzed standardized precipitation index (SPI) and standardized runoff index (SRI) respectively. The best-fit copula family was selected to construct the joint probability distribution (JPD) of the SPI and SRI, and MSDI was developed. SPI, SRI, and MSDI at 6 and 12-month drought time scales were analyzed to characterize hydrological drought properties. The correlation among three drought indices (SPI, SRI, and MSDI) were analyzed using the Pearson correlation method. The goodness-of-fit test result showed that the Clayton copula was found the best-fitted copula function in describing JPD the two drought indices. The MSDI showed that the drought onset most likely similar to the SPI. Moreover, MSDI showed the maximum duration of drought occurred with varying severities about 26–28-months, while the duration of drought is extensive, but the frequency of drought less relative to SPI and SRI. The developed model, MSDI had a high correlation with SPI and SRI $$(R>0.7 \mathrm\,\text{and}\,{R}^{2}>0.5, p \sim 0.0)$$ compared to the correlation between SPI and SRI. Therefore, modeling hydrological drought using multiple variables is better than estimated with a single variable.