## 2 Materials and Methods
### Mass Balance Model Based on Separating \(pco_{2}\)-Controlling Processes
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Sampling Date** & \(\theta\) (\({}^{\circ}\)C) & \(\mathbf{S}\) & **TA (\(\mu\)mol kg\({}^{-1}\))** & **DIC (\(\mu\)mol kg\({}^{-1}\))** \\ \hline CDW & 27.76 \(\pm\) 0.20 & 7.88 \(\pm\) 0.28 & 1898 \(\pm\) 3.6 & 1863 \(\pm\) 3.6 \\ KSW & 29.49 \(\pm\) 0.10 & 33.22 \(\pm\) 0.33 & 2232 \(\pm\) 4.4 & 1808 \(\pm\) 0.6 \\ KSSW & 19.48 \(\pm\) 0.09 & 34.11 \(\pm\) 0.05 & 2244 \(\pm\) 0.6 & 2105 \(\pm\) 13 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Three end-member characteristics of water mass from measurements obtained during cruises in July and August 2006. According to the definition, the NEP calculation formula is  
\[\text{NEP}=-\Delta\text{DIC}_{\text{bio}}/\Delta\text{t} \tag{23}\]  
The NEP values in or under the mixed layer (mmol C m\({}^{-2}\) day\({}^{-1}\)) were calculated using the integral of the NEP over different water layers (mmol C m\({}^{-3}\) day\({}^{-1}\)). Finally, we calculated the CO\({}_{2}\) flux caused by biological processes and its contribution to the air-sea CO\({}_{2}\) exchange flux as  
\[\text{F}_{\text{CO2 bio}}=\text{k}\times\text{K}_{0}\times\Delta p\text{CO}_{ \text{2 bio}} \tag{24}\]  
\[\text{F}_{\text{CO2 non-bio}}=\text{F}_{\text{CO2}}-\text{F}_{\text{CO2 bio}} \tag{25}\]  
\[\text{Cont}=(\text{F}_{\text{CO2 bio}}/\text{F}_{\text{CO2}})\times 100\% \tag{26}\]  
where \(\text{F}_{\text{CO2 bio}}\) is the change in CO\({}_{2}\) flux caused by biological processes (mmol m\({}^{-2}\) day\({}^{-1}\)) and \(\text{F}_{\text{CO2 non-bio}}\) is the change in CO\({}_{2}\) flux caused by other processes. \(\text{F}_{\text{CO2 bio}}>0\) indicates that biological processes, such as the degradation of organic matter by microorganisms, cause seawater to release CO\({}_{2}\). \(\text{F}_{\text{CO2 bio}}<0\) indicates that biological processes, such as absorption of CO\({}_{2}\) by phytoplankton photosynthesis, cause seawater to absorb CO\({}_{2}\) from the atmosphere. Cont is the contribution of CO\({}_{2}\) flux changes caused by biological processes to the air-sea CO\({}_{2}\) exchange flux. Cont \(>0\) means that the variation in CO\({}_{2}\) caused by biological processes has the same direction as the variation in air-sea CO\({}_{2}\) exchange, which indicates a positive feedback progress; Cont \(<0\) indicates a negative feedback progress. Under the mixed layer, potential \(p\)CO\({}_{2}\) and \(p\)CO\({}_{\text{2 bio}}\) were evaluated with the CO2 SYS program using DIC\({}_{2}\), TA\({}_{2}\), S\({}_{2}\), T\({}_{2}\) and (DIC\({}_{2}\))\({}_{\text{bio}}\), TA\({}_{1}\), S\({}_{1}\), and T\({}_{1}\), respectively. *F\({}_{\text{CO2}}\) and *F\({}_{\text{CO2 bio}}\) for each depth were calculated using Equations (1) and (23), and then the potential carbon flux (*F\({}_{\text{CO2}}\)) and the potential carbon flux caused by biological processes (*F\({}_{\text{CO2 bio}}\)) in the three regions at each time point were integrated for the water layers beneath the MLD. Figure 2: Scatter plots of potential temperature and salinity: M4-1 (triangles), M4-8 (squares), and M4-13 (circles). The labeled vertices denote the three end-members from the three water masses: Changjiang diluted water (CDW), Kuroshio surface water (KSW), and Kuroshio subsurface water (KSSW). Isoclines of potential density are shown in this figure.