Drought, one of the main factors threatening social life today, is examined and analyzed by its types such as meteorological, agricultural, and hydrological droughts. Thus, decision-makers need advanced methods in monitoring and assessing the drought, which is important for future plans. Multivariate drought indices were developed to allow determining the actual and real level of drought by reducing the deficiencies of current methods. In a region having three different characteristics (BSk: semiarid cold, Csa: dry summer-hot summer, and H: unclassified highland), MSDI was modeled by utilizing the data from Standardized Precipitation Evapotranspiration Index (SPEI) and Standardized Surface Runoff Index (SRI). For the period between 2003 and 2021, the precipitation, evapotranspiration, and surface runoff data were obtained from SPEI Global Drought Monitor and ERA5 databases. Gaussian function was used in establishing the copula-based joint distribution functions according to AIC, BIC, and max-likelihood assessment criteria. The R packages offering a wide range of use for drought modeling and assessment based on the multivariate drought indices were used. The calculations performed for 4 different time scales as MSDI 1-3-6-12 (soil moisture, surface hydrology, and agricultural and hydrological perspectives) showed acceptable performance in multivariate estimation of the drought. It was determined that, for all four time scales (1, 3, 6, and 12 months), MSDI values obtained from modeling were more similar to SPEI values in comparison with SRI values. Considering all the data, it was determined that the years 2007 and 2016 were found to be the driest years for the basin on the 6-month scale, whereas the years 2016 and 2021 were the driest years on the 12-month scale.