## 2 Materials and Methods
### Mass Balance Model Based on Separating \(pco_{2}\)-Controlling Processes  
The volumetric flow equation [31] was used to calculate the air-sea CO\({}_{2}\) exchange flux:  
\[\mathrm{F_{CO2}=k\times K_{0}\times(\mathrm{\rho CO_{2 water}-\mathrm{\rho CO_{2 air}}})} \tag{2}\]  
where \(p\)CO\({}_{2\mathrm{air}}\) and \(p\)CO\({}_{2\mathrm{water}}\) are the partial pressures of CO\({}_{2}\) in the atmosphere and surface water (uatm), respectively; \(p\)CO\({}_{2\mathrm{air}}\) was 380 and 377 uatm 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). FCO\({}_{2}\) is the air-sea CO\({}_{2}\) exchange flux (mmol m\({}^{-2}\) day\({}^{-1}\)), where FCO\({}_{2}\) > 0 indicates that seawater releases CO\({}_{2}\) into the atmosphere, and F\({}_{\mathrm{CO2}}\) < 0 means that seawater absorbs atmospheric CO\({}_{2}\). K\({}_{0}\) is the solubility coefficient of CO\({}_{2}\) in seawater [32], and k is the gas transfer velocity. For short-term wind, k was calculated using the empirical formula proposed by [PERSON] [33] and revised by [PERSON] [34]:  
\[\mathrm{k=0.27\times U_{10}}^{2}\times(\mathrm{Sc/660})^{-0.5} \tag{3}\]  
\[\mathrm{Sc=Sc_{0}\times(1+3.14S/1000)} \tag{4}\]  
\[\mathrm{Sc_{0}=0.0476T^{3}+3.7818T^{2}-1.201T+1800.6} \tag{5}\]  
where U\({}_{10}\) is the wind speed (m s\({}^{-1}\)) at a height of 10 m above the sea surface (Remote Sensing Systems, CCMP Wind Vector Analysis Product, [[http://www.remss.com/measurements/ccmp/](http://www.remss.com/measurements/ccmp/)]([http://www.remss.com/measurements/ccmp/](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 (t\({}_{1}\)), the sea surface temperature (SST), sea surface salinity (SSS), and carbonate system parameters, including dissolved inorganic carbon (DIC), total alkalinity (TA), and \(p\)CO\({}_{2}\), are T\({}_{1}\), S\({}_{1}\), TA\({}_{1}\), DIC\({}_{1}\), and (\(p\)CO\({}_{2}\))\({}_{1}\), respectively. At time t\({}_{2}\), the above parameters are change to T\({}_{2}\), S\({}_{2}\), TA\({}_{2}\), DIC\({}_{2}\), and (\(p\)CO\({}_{2}\))\({}_{2}\). \[\Delta p\mathrm{CO_{2}}=(p\mathrm{CO_{2}})_{2}-(p\mathrm{CO_{2}})_{1}=\Delta p \mathrm{CO_{2}}_{\mathrm{item}}+\Delta p\mathrm{CO_{2a-s}}+\Delta p\mathrm{CO _{2 mix}}+\Delta p\mathrm{CO_{2 bio}}+\Delta p\mathrm{CO_{2 non}} \tag{6}\]  
\[\Delta\mathrm{DIC=\Delta DIC_{a-s}+\Delta DIC_{mix}+\Delta DIC_{bio}} \tag{7}\]  
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 CO\({}_{2}\) from organic matter degradation by microbes and CO\({}_{2}\) uptake by phytoplankton), respectively. \"\(\Delta\)\" refers to the change in a particular parameter within a certain period of time (from t\({}_{1}\) to t\({}_{2}\)). On a short timescale (three hours or each day), the nonlinear term (\(\Delta p\mathrm{CO_{2 non}}\)) is essentially zero. The four different factors in Equation (6) were calculated as described below. First, the thermal effect on \(\Delta p\mathrm{CO_{2}}\) was calculated by Equation (8). \[\Delta p\mathrm{CO_{2 tem}}=(p\mathrm{CO_{2}})_{1}\times\exp\ (0.0423\times(\mathrm{T_{2}-T_{1}}))-(p \mathrm{CO_{2}})_{1} \tag{8}\]  
where 0.0423 is the temperature dependence coefficient of \(p\)CO\({}_{2}\) presented by [PERSON] [38]. Second, air-sea CO\({}_{2}\) exchanges only change DIC and \(p\)CO\({}_{2}\) but have no effect on TA.