Mathematical modeling for interactions and transport of particulate bioavailable phosphorus with sediment in the Yarlung Tsangpo River

Particulate bioavailable phosphorus (PBAP) plays a critical role in biogeochemical cycling and primary productivity in aquatic ecosystems, particularly in ecologically vulnerable alpine regions such as the Yarlung Tsangpo River. However, the understanding of PBAP dynamics remains limited due to the complex interaction and transport processes. To address this gap, we developed a mathematical model that integrated hydrodynamics, sediment transport, and the dynamics of dissolved and particulate phosphorus to investigate PBAP transport with sediment.  PBAP bound to sediment was represented by coupling sediment mineral properties and environmental factors. Lateral inputs of water, sediment, and phosphorus from the watershed were incorporated using the Soil and Water Assessment Tool (SWAT). The model was applied to the Yarlung Tsangpo River and successfully reproduced PBAP distributions, with spatiotemporal concentrations ranging from 0.20 to 0.38 mg g−1, consistent with field measurements. The estimated annual PBAP flux was 2.77 Gg yr−1, partitioned as 46.0% Ex‑P, 37.7% Fe‑P, and 16.3% Al‑P, which exceeded the flux of dissolved phosphorus (~0.80 Gg yr−1). Furthermore, over 95% of annual PBAP flux occurred between June and September, indicating strong temporal variability in PBAP dynamics within monsoonal alpine basins. This model advances process-based quantifications of PBAP dynamics and has far-reaching implications for water resources research and management.