As a natural hazard, drought is a complex multivariate phenomenon that requires more comprehensive analysis. In this study, we studied meteorological, agricultural, and hydrological drought events with precipitation, soil moisture, and stream flow data for the study area. The risk analysis for drought duration and severity of three kinds of drought events were analyzed with univariate and three kinds of bivariate return periods based on the copula. Furthermore, the propagation of three kinds of drought was studied. From the investigation, it is observed that agricultural drought events are longer and more severe, besides the risk associated with agricultural drought is high compared to other kinds of drought. Moreover, the average time taken for meteorological drought to propagate into agricultural drought is 4.3 months and for the hydrological drought is 3.8 months for the river basin. The comprehensive study of three kinds of drought is helpful to adopt suitable drought management plans in the region.

The degradation of land and increasing water scarcity are existing challenges for agricultural sustainability, necessitating the implementation of improved soil-conservation practices at the watershed scale. The identification and selection of critical/prone areas based on erosion-governing criteria is essential and helps in the execution of the management process for determining priority. This study prioritizes erosion-prone sub-watersheds (alternatives) based on morphometric parameters (multiple criteria) via five Multi-Criteria Decision Analysis (MCDA) approaches, i.e., AHP: Analytical Hierarchy Process; TOPSIS: Technique for Order of Preference by Similarity to Ideal Solution; VIKOR: VIseKriterijumska Optimizacija I Kompromisno Resenje; SAW: Simple Additive Weighting; and CF: Compound Factor. Based on their priority score, 19 sub-watersheds were classified into four priority classes: low priority (0–0.25), moderate priority (0.25–0.50), high priority (0.50–0.75), and very high priority (0.75–1). The results revealed that about 8.34–30.15% area of the Burhanpur watershed is critically prone to erosion, followed by 23.38–52.05% area classed as high priority, 7.47–49.99% area classed as moderate priority, and 10.33–18.28% area classed as low priority. Additionally, four indices—percentage of changes (∆P), intensity of changes (∆I), the Spearman rank correlation coefficient test (SCCT), and the Kendall tau correlation coefficient test (KTCCT)—were employed to compare the models. This study confirms the efficacy of morphometric parameters for prioritizing sub-watersheds to preserve soil and the environment, particularly in areas for which limited information is available.