A fluorescence index-informed δ¹⁸Oₚ-based Bayesian mixing framework for quantifying riverine phosphorus sources

Quantifying the contributions of different phosphorus (P) sources is critical for controlling eutrophication, yet source discrimination using phosphate oxygen isotopes (δ¹⁸Oₚ) alone often involves significant uncertainty due to overlapping isotopic signatures. To address this, we developed a fluorescence index (FI)-informed Bayesian mixing model for δ¹⁸Oₚ, providing a pragmatic approach for watershed-scale P source discrimination. In this framework, δ¹⁸Oₚ defined the mixing likelihood, while FI supplied auxiliary information to construct period-specific informative Dirichlet priors. Applied to the Yongan River watershed in eastern China, this framework refined source allocation where isotopic discrimination was limited and reduced 90% posterior uncertainty intervals by 11-20% relative to the δ¹⁸Oₚ-only baseline model. Source contributions showed distinct seasonal shifts, with riparian soils and agricultural runoff dominating P inputs during high-flow conditions, whereas groundwater became increasingly important during normal and low-flow periods. These flow-dependent patterns were qualitatively consistent with independent hydrological and hydrochemical evidence under varying flow regimes. A decoupled stress test indicated that the inferred period-specific source structure was generally preserved under plausible non-conservative and asynchronous alteration of δ¹⁸Oₚ and FI. Overall, these findings indicate that FI can serve as a complementary hydro-biogeochemical indicator for improving the precision and interpretation of δ¹⁸Oₚ-based P source apportionment.