On the role of ²¹⁰Bi in the apparent disequilibrium of ²¹⁰Pb-²¹⁰Po at sea

The disequilibrium of the grandparent-daughter pair ²¹⁰Pb (t_1/2=_{22.3 years})-²¹⁰Po (t_{1/2=138 days}) has been used to estimate the export fluxes of particulate organic carbon in the ocean using particulate-matter-associated ²¹⁰Po. ²¹⁰Po is produced from ²¹⁰Bi, not from ²¹⁰Pb. The half-life of ²¹⁰Bi (t_{1/2=5.01 days}) is sufficiently long compared to the rates of biological particle formation and decomposition or dissolution occurring at sea. The role of ²¹⁰Bi has not yet been assessed quantitatively in the apparent disequilibrium between ²¹⁰Pb and ²¹⁰Po, partly due to the non-existence of ²¹⁰Bi depth profile measurements at sea up to now. However, greater affinity of ²¹⁰Bi over ²¹⁰Po and ²¹⁰Pb was found recently in coastal waters and phytoplankton ²⁰⁷Bi uptake experiments. Build upon these findings, we developed a primitive and simple analytical approach to elucidate the role of ²¹⁰Bi in the ²¹⁰Po-²¹⁰Pb pair in the ocean using a simplified two-box irreversible steady-state ocean model. We assumed that the activity concentrations in the dissolved and particulate phases of ²¹⁰Pb, ²¹⁰Bi, and ²¹⁰Po in a given water column are solely determined by the concentration of the particles, their input and output, the distribution coefficients between dissolved and particulate phases, and decay constants of these radionuclides in the steady-state ocean. The ²¹⁰Bi contribution to the ²¹⁰Pb-²¹⁰Po activity difference in seawater is found to be significant, therefore, it needs to be considered in estimating particle fluxes using ²¹⁰Pb-²¹⁰Po secular equilibrium at sea.