Proposing a new integration system: Tolerance Merged Collocation comparative to Modified and Scaled Triple Collocation and weighting scheme to integrate four indices

The absence of a global standard for drought assessment has led to inconsistencies in observational methods. This study explores recent advancements in merging techniques to enhance drought monitoring, develop more reliable indices, and introduce a weighting scheme for integrating four variables, extending existing methodologies for improved drought assessment. To achieve this, we analyzed three standardized drought indices (SPI, SPTI, and SPEI) across six northern regions of Pakistan from 1971 to 2017. We introduced Tolerance Merged Collocation (TMC) and integrated it with Modified Triple Collocation (MTC) and Scaled Triple Collocation (STC), extending these techniques to accommodate four variables for a more comprehensive drought evaluation. The effectiveness of the Merged Drought Indices (MDI) was assessed using Exploratory analysis, Taylor diagrams, Sen's slope, Feature Similarity Index (FSI), Index of Agreement (IOA), d2 statistics, Target Diagrams, and Kling-Gupta Efficiency (KGE). This study validates that the TMC-based MDI provides a more effective quantitative approach for consolidating multiple drought indices. Furthermore, the introduction of a novel weighting scheme and the extension of existing techniques to four variables enhance the precision and reliability of drought assessment, ensuring a more robust framework for future research and real-time monitoring.