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 (R2) 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. *Corresponding author: E-mail: [email protected]; phone: (443) 482-2348. Current address: Smithsonian Environmental Research Center, 647 Contees Wharf Rd, Edgewater, MD, 21037-0028. Acknowledgments We thank Kevin Arrigo, Nick de Sieyes, Eric Grossman, Daniel Keymer, Blythe Layton, Kate Maher, Pere Masqué, Holly Michael, Lauren Sassoubre, Joseph Street, Emily Jan Viau, Sarah Walters, Kevan Yamahara, and two anonymous reviewers for comments that led to the improvement of this manuscript. Tim Julian and Stanford Statistics Consulting provided statistical assistance, Gwyneth Hughes provided MATLAB support, and William Burnett, Matthew Charette, and Henrieta Dulaiova graciously provided raw data from their published and unpublished work for review and reanalysis. DOI 10:4319/lom.2011.9.380 Limnol. Oceanogr.: Methods 9, 2011, 380–395 © 2011, by the American Society of Limnology and Oceanography, Inc. LIMNOLOGY and OCEANOGRAPHY: METHODS mixed estuary (Eq. 2; Moore et al. 2006). Water age (T), or the amount of time that has elapsed since Ra became disconnected from its source (aquifer substrate) and entered the coastal ocean, can be calculated as: