Radar precipitation information with high spatial and temporal resolution is essential for flood forecasting, urban pluvial flood warning, and digital twin basins, yet radar quantitative precipitation estimation (QPE) is affected by observational errors, retrieval relationships, terrain effects, and multi-source merging. Based on 1328 Web of Science Core Collection publications (2000–2025), this study integrates bibliometric analysis, Transformer-based semantic representation, BERTopic modeling, semantic association analysis, and bibliographic coupling to map the topic structure, thematic evolution, and methodological lineages of research on radar precipitation uncertainty and hydrological applications. Nineteen micro-level topics were identified and grouped into four categories: measurement error identification and correction, uncertainty characterization and modeling, error propagation and scale effects, and operational applications and risk decision-making. The semantic structure shows that observation and correction and hydrological propagation constitute the main branches, while AI-driven forecasting is emerging. Methodological lineage analysis indicates that Statistical Fusion dominates the field, Physics provides a foundation, and AI and Hybrid methods have grown markedly in recent years, with Hybrid methods bridging physical mechanisms, statistical fusion, and data-driven approaches. Future research should integrate explainable AI, physical constraints, probabilistic modeling, and hydrological-response consistency testing to advance chain-wide uncertainty representation from observation and forecasting to hydrological propagation and risk-informed decision-making.