Abstract: The three-body scatter signature (TBSS) is a critical indicator for the detection of large hail (diameter is greater than 20 mm) using S-band Doppler weather radar. It is characterized by spurious echoes resulting from a triple-scattering processes: Initial scattering in the hail region, ground reflection, and secondary scattering back through the hail region. To improve hail warning accuracy and mitigate TBSS-induced artifacts in quantitative precipitation estimation, the development of automated TBSS identification algorithms is essential. A limitation in previous algorithmic is the imposition of an artificial constraint, whereby grid points with a horizontal polarization reflectivity factor (Z_H) no more than 25 dBZ are classified as TBSS regions, and this inherently limits detection when the signature is obscured by genuine precipitation echoes exceeding this threshold.An innovative dual-polarization algorithm named TBSS-RFK is introduced, which synergistically combines random forest classification with K-means clustering to overcome these limitations. The methodology leverages a comprehensive dataset comprising 930 carefully validated cases (465 TBSS and 465 non-TBSS samples), derived from large hail events observed across Hunan Province from 2021 to 2025. For each event, three key dual-polarization parameters are extracted: The horizontal polarimetric reflectivity factor (Z_H), differential reflectivity (Z_DR), and correlation coefficient. The algorithm is designed to automatically identify TBSS grid points at a 1°×1 km resolution, followed by a comprehensive performance evaluation and application case analysis.Built upon a comprehensive understanding of TBSS formation mechanisms, polarimetric characteristics, and physical essence, TBSS-RFK algorithm successfully addresses the long-standing challenge of detecting TBSS obscured by genuine precipitation echoes. The algorithm achieves exceptional performance metrics with 96.6% probability of detection (POD), 6.5% false alarm ratio (FAR), and 90.5% critical success index (CSI). Compared with conventional single-polarization TBSS detection algorithms, TBSS-RFK demonstrates significant improvements by a 16% reduction in FAR and a 20.5% enhancement of CSI.Feature selection constitutes the cornerstone of TBSS-RFK algorithm's success. The availability of dual-polarization radar parameters enables robust identification of precipitation-embedded TBSS, with Z_H and correlation coefficient identified as particularly diagnostic. Statistical analysis reveals that 50% of confirmed TBSS grid points are characterized by low-value thresholds: Z_H not exceeding 15.0 dBZ, Z_DR not exceeding 0.19 dB, and correlation coefficient not exceeding 0.84. Through rigorous examination of these polarimetric signatures and their physical interpretations, the algorithm strategically employs low-value regimes of Z_H, Z_DR, and correlation coefficient as primary detection features, with correlation coefficient emerging as the most statistically significant discriminator. This physics-informed feature engineering approach underpins the algorithm's superior performance.By transforming complex image recognition into an efficient binary classification task through meteorologically informed feature engineering, TBSS-RFK algorithm provides a robust operational solution and offers insights for developing lightweight machine learning algorithms. A primary limitation is that the algorithm's validation is based on 465 samples from Hunan Province, leaving its generalizability to other geographic/climatic regions unexplored. Future work will be directed toward assessing its stability with larger datasets.