<p>The water age in coastal waters can be estimated by a simplified formula defined by activity ratio of radium isotopes when neglecting the effects of four factors including recirculated seawater (RSGD), open sea water end-member, sediments and rivers. Although this formula has been widely used,&#160;sometimes it is applied without checking the assumptions of neglecting the effects of the above-mentioned four factors.&#160;Here an attempt is made to give a generalized formula for estimating water age explicitly incorporating all the above-mentioned effects. The formula is then applied in Daya Bay, China by comprehensively using all the radium quartet (<sup>223,224,226,228</sup>Ra) data to assess the water age and submarine groundwater discharge (SGD). Data analyses indicate that the factors such as RSGD, open sea water end-member, sediments and rivers should be included in the general radium model when there are various radium sources and their contributions are unknown. It is found that&#160;in Daya Bay, neglecting the effects of RSGD underestimates the water age by 25.5-45.7% and neglecting the effects of open sea water end-member&#160;overestimates the water age by 120-130%. The SGD-derived fluxes of nutrients and trace elements are significantly higher than those from local rivers. SGD can support approximately&#160;63-70% of the total primary production. Overall, this study emphasizes again the importance of the general radium model and enhances accuracy in estimating water age and SGD. Our results also reveal that&#160;SGD&#160;significantly&#160;influences&#160;coastal primary production&#160;in Daya Bay and other similar aquatic ecosystems.</p>
Quantification of the water age and submarine groundwater discharge in a typical semi-enclosed bay: Using stable oxygen (18O) and radioactive radium (228Ra) isotopes