Dust storms pose a critical environmental and public health challenge in arid and semi-arid regions, particularly in Hormozgan Province, Iran. This study aimed to evaluate the importance of drought indices and their underlying variables in explaining the variability of the Aerosol Optical Depth (AOD) dust indicator. Monthly time series from 2001 to 2023 (264 observations per pixel) for 13 environmental variables, including Pr, SPI, ET, T, soil moisture, vegetation indices (NDVI, EVI, VCI, VHI), and AOD, were analyzed spatially. The applied methodologies included Impact Threshold Analysis, spatial correlation (Pearson), global sensitivity analysis (PAWN, Sobol, FAST), gradient- and perturbation-based sensitivity analysis, and Random Forest (RF) modeling for assessing relative feature importance and conducting partial dependence analysis. Key findings reveal that Pr and ET are the strongest controls on dust activity, with combined sensitivity scores of 100% and 74.8%, respectively. Maximum AOD occurs under conditions of very low precipitation (similar to 4.66 mm) and high ET (>0.96 mm). The impact range of ET (7.70 units) and soil moisture (5.55 units) on AOD is substantially wider than that of other variables, indicating the long-term sensitivity of dust to aridity and intense evaporation. In contrast, vegetation indices (e.g., NDVI, EVI, VCI) exhibit very narrow impact ranges (<0.42 units), exerting a significant influence on dust only under critical conditions of very weak vegetation cover or bare soil. Spatial correlations confirm that SPI and Pr have the highest positive correlations with AOD (0.418 and 0.404, respectively), while relationships are predominantly nonlinear (absence of strong correlation >0.5). The RF model corroborates the dominance of ET and Pr in predicting AOD (feature importance similar to 0.23 and similar to 0.22, respectively). The multi-method sensitivity analysis synthesis identified Pr as the most consistently important variable. ET demonstrated strong sensitivity in derivative-based models, while T was prominent in global sensitivity analyses. Among drought indices, SPI/PDSI showed higher sensitivity than others. Consequently, the underlying variables of drought indices (particularly low Pr and high ET) play a more determinant role in regional dust occurrence than vegetation parameters. These findings emphasize that dust management strategies should focus on reducing ecosystem vulnerability through the concurrent spatio-temporal monitoring of ET and soil moisture, rather than relying solely on enhancing vegetation cover. Furthermore, employing multiple sensitivity analysis methods is essential for result validation, as each method reveals different aspects of the nonlinear relationship between the variables and AOD.