Machine learning-enhanced game theory composite drought index for reliable drought monitoring and forecasting in cold Mediterranean mountain climates

A reliable composite drought index is essential for effective drought monitoring. This study used game theory to develop a spatially variable weighted drought index (GTDI) that combines the Standardized Precipitation-Evapotranspiration Index (SPEI) and the Standardized Soil Moisture Index (SSMI). Precipitation, temperature, and soil moisture data came from ERA5-Land for Lorestan Province (1969–2020). We calculated SPEI and SSMI on a 3-month timescale and obtained the GTDI by solving a system of linear equations. The GTDI was near-normally distributed (mean −0.038, SD 0.962). Its correlation with SPEI (0.97, p < 0.001) was stronger than with SSMI (0.83, p < 0.001), which points to meteorological drivers as the main influence. Average drought intensity in dry months was 1.57, and the longest drought lasted three months. Seasonally, the most severe droughts occurred in autumn (−0.90) and summer (−0.80). K-means clustering identified four patterns: severe summer drought (32.3%), moderate winter drought (32.2%), mild autumn drought (18.0%), and spring non-drought conditions (17.2%). The Mann–Kendall test showed no significant annual trend (Z = −0.885, p = 0.374), though 10-year moving windows suggested drying trends in the mid-1980s and early 2000s. A Random Forest forecast for 2021–2025 gave high accuracy (R 2 = 0.9114, RMSE = 0.2876, MAE = 0.2008). Feature importance analysis ranked the 12-month lagged GTDI as the top predictor (74.1%). The forecast pointed to a mean GTDI of about −0.208, with severe drought in 12 months. The GTDI appears useful for monitoring and predicting drought in semi-arid regions with cold Mediterranean mountain climates. But these results are specific to Lorestan Province; more cross-regional work is needed to test broader applicability. Independent validation against ground-based measurements and drought impact data also remains a priority for future research.