Using radium isotopes to characterize water ages and coastal mixing rates: A sensitivity analysis

Numerous studies have used naturally occurring Ra isotopes ( ²²³Ra, ²²⁴Ra, ²²⁶Ra, and ²²⁸Ra, with half-lives of 11.4 d, 3.7 d, 1600 y, and 5.8 y, respectively) to quantify water mass ages, coastal ocean mixing rates, and submarine groundwater discharge (SGD). Using Monte Carlo models, this study investigated how uncertainties in Ra isotope activities and the derived activity ratios (AR) arising from analytical uncertainty and natural variability affect the uncertainty associated with Ra-derived water ages and eddy diffusion coefficients, both of which can be used to calculate SGD. Analytical uncertainties associated with ²²⁴Ra, ²²⁶Ra, and ²²⁸Ra activities were reported in most published studies to be less than 10% of sample activity; those reported for ²²³Ra ranged from 7% to 40%. Relative uncertainty related to natural variability-estimated from the variability in ²²³Ra and ²²⁴Ra activities of replicate field samples-ranged from 15% to 50% and was similar for ²²³Ra activity, ²²⁴Ra activity, and the ²²⁴Ra/ ²²³Ra AR. Our analysis revealed that AR-based water ages shorter than 3-5 d often have relative uncertainties greater than 100%, potentially limiting their utility. Uncertainties in eddy diffusion coefficients estimated based on cross-shore gradients in short-lived Ra isotope activity were greater when fewer points were used to determine the linear trend, when the coefficient of determination (R ²) was low, and when ²²⁴Ra, rather than ²²³Ra, was used. By exploring the uncertainties associated with Ra-derived water ages and eddy diffusion coefficients, this study will enable researchers to apply these methods more effectively and to reduce uncertainty.