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The main aim of this study is to characterize and monitor drought distribution and expansion over Upper Blue Nile of Ethiopia by using univariate standard precipitation index (SPI) and standardized soil moisture index (SMI) whose joint distribution leads to multi standardized drought index (MSDI). The soil moisture and CHIRPS precipitation data from first January 1980 to 2016 are modeled. The indices of SPI, SMI and the joint MSDI value over the Upper Blue Nile are analyzed. The SPI for different time scales is implemented. The correlation between severity, duration and intensity including wetness and drought strengths is computed and analyzed. It is found that the correlation between duration and severity is 0.96 and normal conditions for SPI 3, 6, 12 month time scales are frequently observed rather than moderate, severe and extreme severe drought or wetness. Building on soil moisture and precipitation data of the summer season, the Clayton copula model is selected based on goodness of fit parameters. After setting the best copula family for the Upper Blue Nile then we applied the joint distribution method is applied for characterizing and monitoring drought. It is found that the MSDI more clearly showed that the severity of drought across the time series of each time scales, than SPI and SMI. As the time scale increases there is decline of fluctuation or frequency of drought and the rising of drought duration is shown by SPI, SMI and MSDI. By using SPI6, SMI6 and MSDI6 the spatial distribution of drought is determined from June to August in the years 1984 and 2015 indicate the drought expansions in the eastern and western parts of Upper Blue Nile during the respective years.