<p>Defining droughts using only one variable or index such as precipitation, soil moisture, or runoff might not be enough for accurate risk assessment and decision-making. In this study, a multivariate and multi-criteria drought modeling approach called the Multivariate Standardized Drought Index (MSDI) was used and short-term drought time frames of one, three, and six months were considered. The MSDI index was calculated using precipitation and volumetric soil layer data of Sakarya for the period 1940–2024. Machine learning (ML)-based forecasting models were applied to more accurately anticipate future drought episodes by utilizing the calculated MSDI index. In the prediction models, t − 1, t − 2, and t − 3 input variables were used to predict the drought index at t output variable. Gaussian process regression (GPR), support vector machine regression, bootstrap aggregation, and least squares boosting methods were used. To generate hybrid models, pre-processing methods such as tunable Q-factor wavelet transform (TQWT), maximal overlap discrete wavelet transform (MODWT), and variation mode decomposition (VMD) were applied. Model performance was evaluated using seven distinct performance criteria. Multiple performance metrics such as Mean Absolute Error (MAE), Root Mean Square Error (RMSE), Relative Root Mean Square Error (RRMSE), Coefficient of Determination (R²), Nash–Sutcliffe Efficiency (NSE), Kling–Gupta Efficiency (KGE), Overall Index (OI) were used to determine the success of the models. The hybrid TQWT-GPR model achieved the best performance across different time scales: for the 1-month time scale, it yielded RRMSEE = 8.080, KGE = 0.998, and NSE = 0.997; for the 3-month time scale, it achieved RRMSEE = 6.754, KGE = 0.997, and NSE = 0.997; and for the 6-month time scale, it demonstrated the highest accuracy with RRMSEE = 3.70, KGE = 0.995, and NSE = 0.999. The decomposition success of TQWT was found to be higher than that of VMD and MODWT when all performance factors were considered.</p>