Development of a Drought Assessment Index Coupling Physically Based Constraints and Data-Driven Approaches

To improve the physical consistency and interpretability of traditional drought indices, this study proposes a drought assessment model that couples physically based constraints with data-driven approaches, leading to the development of a Multivariate Drought Index (MDI). The model employs convolutional neural networks to achieve physically consistent downscaling, thereby obtaining a high-resolution Normalized Difference Water Index (NDWI), Temperature Vegetation Dryness Index (TVDI), Vegetation Condition Index (VCI), and Temperature Condition Index (TCI). Objective weights are determined using the Criteria Importance Through Intercriteria Correlation method, while random forest and Shapley Additive Explanations are integrated for nonlinear interpretation and physics-guided calibration, forming an ensemble framework that incorporates multi-source and multi-scale factors. Validation with multi-source data from 2000 to 2024 in the major maize-growing areas of Heilongjiang Province demonstrates that MDI outperforms single indices and the Vegetation Health Index (VHI), achieving a correlation coefficient (r = 0.87), coefficient of determination (R2 = 0.87), RMSE (0.08), and classification accuracy (87.4%). During representative drought events, MDI identifies signals 16–20 days earlier than the Standardized Precipitation Evapotranspiration Index (SPEI) and the Soil Moisture Condition Index (SMCI), and effectively captures localized drought patches at a 250 m scale. Feature importance analysis indicates that the NDWI and TVDI are consistently identified as dominant factors across all three methods, aligning physically interpretable analysis with statistical contribution. Long-term risk zoning reveals that the central–western region of the study area constitutes a high-risk zone, accounting for 42.6% of the total. This study overcomes the limitations of single indices by integrating physical consistency with the advantages of data-driven methods, achieving refined spatiotemporal characterization and enhanced overall performance, while also demonstrating potential for application across different crops and regions.