Water resource management in semiarid regions poses significant challenges due to extreme weather and the vast, complex terrain of river basins, which imposes serious logistical constraints on monitoring and detecting hydrological anomalies. Therefore, remote sensing provides a crucial solution for addressing hydrological anomalies in data-sparse areas. This research aims to estimate hydrological response anomalies via the water balance formula (P-ET) and create a new composite hydrological response anomaly index (CHRAI) by integrating multiple satellite-based datasets, including CHIRPS, Terra Climate, and MODIS, with weights determined using a Random Forest model. Spatiotemporal variability maps of estimated (P-ET) and modeled (CHRAI) hydrological response anomalies were generated for the Oum Er-Rbia River basin (Morocco) for the 2001-2021 period. The composite CHRAI model performance was evaluated based on three hydrological drought indices, which involved mapping comparisons, Pearson's correlation statistical analyses, linear regression, and Taylor diagram analysis. As a result, strong interannual variability in hydrological response anomalies was observed over the entire study area. The comparative mapping of the estimated (P-ET) and modeled (CHRAI) hydrological responses revealed strong spatiotemporal concordance. Additionally, a high correlation (r = 0.87) was observed between the CHRAI, P-ET, and the indices (Flow, SHI, IDF, and DLHI) at the Tamchachat station. Based on the Taylor diagram analysis, the modeled index (CHRAI) demonstrates approximately 90% correlation with the observed index, a high standard deviation (P-ET), and a CRMSE close to 0.4, indicating strong agreement between the developed and estimated model (P-ET). This study introduces a novel approach to modeling hydrological response anomalies and underscores the need for further exploration of this methodology.