Drought, as an extreme climatic event, exert a profound impact on agricultural yield. Iran is severely impacted by the depletion of water resources and the rising frequency of droughts due to its arid to semi-arid climate. The agricultural sector, in particular, contends with inefficient water distribution network. Therefore, the assessment of crops' productivity risk in the face of drought assumes a paramount importance for agriculture management, planning and food security. This study estimated the risk of rainfed wheat yield in the Tabriz region of Iran between 1990 and 2020 using two commonly used drought indices: the standardized precipitation index (SPI) and the standardized precipitation evapotranspiration index (SPEI). Employing copula functions, the results show that, under the same conditions, SPEI in the growing season scale has a stronger kendall non-parametric correlation with the yield of rainfed wheat in this region than SPI. Rainfed wheat yield risk rises by roughly 40% in drought situations, from 30% in non-drought conditions to 70% in drought conditions, based on the likelihood of occurrence of this risk under various drought conditions. In addition, the risk growth rate decreases with increasing drought severity; Therefore, the risk difference between moderate and severe desertification is greater than the risk difference between severe and extreme droughts. The non-linear response of crop yield to drought is highlighted by this trend, and in order to properly inform management and planning strategies, yield risk assessments under different drought conditions must be independently verified.