*2.3. Hydrographic Measurements*

Seawater samples were collected using a rosette water collector. Temperature, salinity, and depth data were measured in situ with a Hydro-bios ®MWS6 conductivity-temperature-depth (CTD) recorder. The data were recorded every three hours and monitored continuously for 24 hours. pH was measured with an ORION Ross-type combination electrode, which was calibrated on the NBS scale. The measurement precision was ±0.01 pH units. Total alkalinity (TA) was calculated using the TA–salinity relationship (equation 1), which was acquired by averaging the slopes and intercepts of the TA–salinity relationships in Table 1. The partial pressures of CO2 (*p*CO2) and dissolved inorganic carbon (DIC) were calculated from pH and TA using the program CO2SYS [28].

$$\text{TA (\text{\textquotedbl{}mol\textquotedbl{}}kg}^{-1}) = (13.38 \pm 0.15) \text{S} + (1788.40 \pm 32.63) \tag{1}$$


**Table 1.** Summary of correlation between total alkalinity (TA, μmol kg−1) and salinity.

### *2.4. Mass Balance Model Based on Separating pCO2-Controlling Processes*

The volumetric flow equation [31] was used to calculate the air–sea CO2 exchange flux:

$$\text{F}\_{\text{CO2}} = \text{k} \times \text{K}\_0 \times (p\text{CO}\_{2\text{water}} - p\text{CO}\_{2\text{air}}) \tag{2}$$

where *p*CO2air and *p*CO2water are the partial pressures of CO2 in the atmosphere and surface water (μatm), respectively; *p*CO2air was 380 and 377 μatm in July and August 2006, respectively (ftp://aftp. cmdl.noaa.gov/data/trace\_gases/co2/flask/surface/co2\_tap\_surface-flask\_1\_ccgg\_month.txt). FCO2 is the air–sea CO2 exchange flux (mmol m<sup>−</sup><sup>2</sup> day−1), where FCO2 > 0 indicates that seawater releases CO2 into the atmosphere, and FCO2 < 0 means that seawater absorbs atmospheric CO2. K0 is the solubility coefficient of CO2 in seawater [32], and k is the gas transfer velocity. For short-term wind, k was calculated using the empirical formula proposed by Wanninkhof [33] and revised by Sweeney [34]:

$$\mathbf{k} = 0.27 \times \mathbf{U}\_{10} \,^2 \times \text{(Sc/660)}^{-0.5} \tag{3}$$

$$\text{Sc} = \text{Sc}\_0 \times (1 + 3.14 \text{S/1000}) \tag{4}$$

$$\text{Sc}\_{0} = 0.0476 \text{T}^{3} + 3.7818 \text{T}^{2} - 1.201 \text{T} + 1800.6 \tag{5}$$

where U10 is the wind speed (m s<sup>−</sup>1) at a height of 10 m above the sea surface (Remote Sensing Systems, CCMP Wind Vector Analysis Product, http://www.remss.com/measurements/ccmp/); Schmidt number (Sc) is expressed as a function of temperature (T, Celsius) and salinity (S, psu) [33,35].

We chose to use the mass balance method [36,37] that was modified for the calculation of NEP. At the initial time (t1), the sea surface temperature (SST), sea surface salinity (SSS), and carbonate system parameters, including dissolved inorganic carbon (DIC), total alkalinity (TA), and *p*CO2, are T1, S1, TA1, DIC1, and (*p*CO2)1, respectively. At time t2, the above parameters are change to T2, S2, TA2, DIC2, and (*p*CO2)2.

$$
\Delta p\text{CO}\_2 = (p\text{CO}\_2)\_2 - (p\text{CO}\_2)\_1 \\
= \Delta p\text{CO}\_{2\text{mem}} + \Delta p\text{CO}\_{2\text{n-6}} + \Delta p\text{CO}\_{2\text{mix}} + \Delta p\text{CO}\_{2\text{bio}} + \Delta p\text{CO}\_{2\text{non}} \tag{6}
$$

$$
\Delta \text{DIC} = \Delta \text{DIC}\_{\text{-}0} + \Delta \text{DIC}\_{\text{-}\text{mix}} + \Delta \text{DIC}\_{\text{-}\text{bio}} \tag{7}
$$

The subscripts "tem", "a-s", "mix", and "bio" of the specific parameter denote temperature, air–sea exchange, mixing, and in situ biological processes (including the release of CO2 from organic matter degradation by microbes and CO2 uptake by phytoplankton), respectively. "Δ" refers to the change in a particular parameter within a certain period of time (from t1 to t2). On a short timescale (three hours or each day), the nonlinear term (Δ*p*CO2non) is essentially zero. The four different factors in Equation (6) were calculated as described below.

First, the thermal effect on Δ*p*CO2 was calculated by Equation (8).

$$
\Delta p \text{CO}\_{2\text{term}} = (p \text{CO}\_2)\_1 \times \exp\left(0.0423 \times (\text{T}\_2 - \text{T}\_1)\right) - (p \text{CO}\_2)\_1 \tag{8}
$$

where 0.0423 is the temperature dependence coefficient of *p*CO2 presented by Takahashi [38].

Second, air–sea CO2 exchanges only change DIC and *p*CO2 but have no effect on TA.

$$
\Delta \text{DIC}\_{\text{-}4\text{-}5} = -\text{F}\_{\text{CO2}} \times \Delta \text{t} / (\text{p} \times \text{MLD}) \tag{9}
$$

$$(\text{DIC}\_2)\_{\text{a-s}} = \text{DIC}\_1 + \Delta \text{DIC}\_{\text{a-s}} \tag{10}$$

$$
\Delta p \text{CO}\_{\text{Zn} \cdot \text{s}} = f((\text{DIC}\_2)\_{\text{a-s}}, \text{TA}\_1, \text{S}\_1, \text{T}\_1) - (p \text{CO}\_2)\_1 \tag{11}
$$

where ρ is seawater density (kg m<sup>−</sup>3), MLD is the mixed-layer depth, and (DIC2)a-s is the DIC concentration at time t2 and is affected only by the air–sea exchange from t1 to t2. The functions *f*((DIC2)a-s, TA1, S1, T1) were calculated using the CO2SYS program [28], and the dissociation constants

were taken from Dickson et al. [39].The evaluation of the mixed-layer depth (MLD) was based on the sigma-*t* criterion proposed by Sprintall [40], and it was calculated as follows:

$$
\sigma\_{\text{t,MLD}} = \sigma\_{\text{t,0}} + \Delta \text{T} \times (\partial \text{t} / \partial \text{T}) \tag{12}
$$

$$
\sigma\_t = \mathfrak{p} - 1000 \tag{13}
$$

where <sup>σ</sup>t,0 is the σt value in the surface layer. ΔT is the desired temperature di fference, and Δ T = 0.5 ◦C in this study. The coe fficient of thermal expansion (∂t/∂T) was calculated from the surface temperature and salinity.

Third, using the interaction with the above-mentioned Kuroshio current, the original sources of the three end-member water masses were determined to be Changjiang diluted water (CDW), Kuroshio surface water (KSW), and Kuroshio subsurface water (KSSW) (Figure 2). The equations and characteristics of the three end-member mixing model are as follows (Table 2).

$$m\_{\rm CDW} + m\_{\rm KSW} + m\_{\rm KSSW} = 1\tag{14}$$

*mCDW* × *SCDW* + *mKSW* × *SKSW* + *mKSSW* × *SKSSW* = S (15)

$$m\_{\rm CDW} \times \theta\_{\rm CDW} + m\_{\rm KSW} \times \theta\_{\rm KSW} + m\_{\rm KSSW} \times \theta\_{\rm KSSW} = \Theta \tag{16}$$

where the subscripts CDW, KSW, and KSSW denote the three end-member water masses CDW, KSW, and KSSW, respectively; *mCDW*, *mKSW*, *mKSSW* respectively denote the proportion of three end-members water masses; *SCDW*, *SKSW*, *SKSSW* and θ*CDW*, θ*KSW*, θ*KSSW* denote the salinity and bit temperature of the three-terminal element, respectively; S and θ denote the measured salinity and potential temperature, respectively. From this calculation, the theoretical values of total alkalinity (TA2)mix and dissolved inorganic carbon (DIC2)mix due to mixing during a given time period (from t1 to t2) can be determined. Further, Δ*p*CO2mixcan be calculated. The equations are

$$m\_{\rm CDW} \times (TA\_2)\_{\rm CDW} + m\_{\rm KSW} \times (TA\_2)\_{\rm KSW} + m\_{\rm KSSW} \times (TA\_2)\_{\rm KSSW} = (\rm TA\_2)\_{\rm mix} \tag{17}$$

$$m\_{\rm CDW} \times (\rm DIC\_2)\_{\rm CDW} + m\_{\rm KSW} \times (\rm DIC\_2)\_{\rm KSW} + m\_{\rm KSW} \times (\rm DIC\_2)\_{\rm KSW} = (\rm DIC\_2)\_{\rm mix} \tag{18}$$

$$
\Delta p \text{CO}\_{2\text{mix}} = f((\text{DIC}\_2)\_{\text{mix}}, (\text{TA}\_2)\_{\text{mix}}, \text{S}\_2, \text{T}\_1) - (p\text{CO}\_2)\_1 \tag{19}
$$

where *(TA2)CDW*, *(TA2)KSW*, *(TA2)KSSW* and *(DIC2)CDW*, *(DIC2)KSW*, *(DIC2)KSSW* denote the TA and DIC concentrations of the three end-member at time t2, respectively.

**Table 2.** Three end-member characteristics of water mass from measurements obtained during cruises in July and August 2006.


Finally, the *p*CO2 changes caused by biological processes ( Δ*p*CO2bio) were calculated from the other DIC changes. Thus,

$$
\Delta \text{DIC}\_{\text{bio}} = \Delta \text{DIC} - (\Delta \text{DIC}\_{\text{a-s}} + \Delta \text{DIC}\_{\text{min}}) \tag{20}
$$

$$(\text{DIC}\_2\text{)}\_{\text{bio}} = \text{DIC}\_1 + \Lambda \text{DIC}\_{\text{bio}} \tag{21}$$

$$
\Delta p \text{CO}\_{2\text{bio}} = f((\text{DIC}\_2)\_{\text{bio}}, \text{TA}\_1, \text{S}\_1, \text{T}\_1) - (p\text{CO}\_2)\_1 \tag{22}
$$

where (DIC2)bio is the theoretical value of DIC at time t2 due to biological processes that occurred during a given time period (from t1 to t2).

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<sup>−</sup><sup>2</sup> day−1) were calculated using the integral of the NEP over different water layers (mmol C m<sup>−</sup><sup>3</sup> day−1).

Finally, we calculated the CO2 flux caused by biological processes and its contribution to the air–sea CO2 exchange flux as

$$\mathbf{F}\_{\rm CC2bio} = \mathbf{k} \times \mathbf{K}\_0 \times \Delta p \mathbf{C} \mathbf{O}\_{2bio} \tag{24}$$

$$\text{F}\_{\text{CO2non-bio}} = \text{F}\_{\text{CO2}} - \text{F}\_{\text{CO2bio}} \tag{25}$$

$$\text{Cort} = (\text{F}\_{\text{CO2bio}} / \text{F}\_{\text{CO2}}) \times 100\% \tag{26}$$

where FCO2bio is the change in CO2 flux caused by biological processes (mmol m<sup>−</sup><sup>2</sup> day−1) and FCO2non-bio is the change in CO2 flux caused by other processes. FCO2bio > 0 indicates that biological processes, such as the degradation of organic matter by microorganisms, cause seawater to release CO2. FCO2bio < 0 indicates that biological processes, such as absorption of CO2 by phytoplankton photosynthesis, cause seawater to absorb CO2 from the atmosphere. Cont is the contribution of CO2 flux changes caused by biological processes to the air–sea CO2 exchange flux. Cont > 0 means that the variation in CO2 caused by biological processes has the same direction as the variation in air–sea CO2 exchange, which indicates a positive feedback progress; Cont < 0 indicates a negative feedback progress.

Under the mixed layer, potential *p*CO2 and *p*CO2bio were evaluated with the CO2SYS program using DIC2, TA2, S2, T2 and (DIC2)bio, TA1, S1, and T1, respectively. \*FCO2 and \*FCO2bio for each depth were calculated using Equations (1) and (23), and then the potential carbon flux (\*FCO2) and the potential carbon flux caused by biological processes (\*FCO2bio) 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.
