Natural disasters such as dust storms are random phenomena created by complicated mechanisms involving many parameters. In this study, we used copula theory for bivariate modeling of dust storms. Copula theory is a suitable method for multivariate modeling of natural disasters. We identified 40 severe dust storms, as defined by the World Meteorological Organization, during 1982–2017 in Yazd province, central Iran. We used parameters at two spatial vertical levels (near-surface and upper atmosphere) that included surface maximum wind speed, and geopotential height and vertical velocity at 500, 850, and 1000 hPa. We compared two bivariate models based on the pairs of maximum wind speed–geopotential height and maximum wind speed–vertical velocity. We determined the bivariate return period using Student t and Gaussian copulas, which were considered as the most suitable functions for these variables. The results obtained for maximum wind speed–geopotential height indicated that the maximum return period was consistent with the observed frequency of severe dust storms. The bivariate modeling of dust storms based on maximum wind speed and geopotential height better described the conditions of severe dust storms than modeling based on maximum wind speed and vertical velocity. The finding of this study can be useful to improve risk management and mitigate the impacts of severe dust storms