The physical model for this study is based on a regional ocean model system (ROMS), which represents an evolution in the family of terrain-following vertical-coordinate models. It solves the primitive equations with hydrostatic and Boussinesq approximations. The ROMS contains innovative algorithms for advection, pressure-gradient force, free-surface variations, and K-profile vertical-mixing parameterizations for surface and bottom boundary layers (Large et al., 1994; Shchepetkin and McWilliams, 2003). For this modeling study, we configured an ROMS circulation model for the northwestern Pacific (NWP, 3°–52°N, 98°–158°E) with (1/12)°×(1/12)° of horizontal resolution, 5 d of temporal resolution and 22 sigma levels (Fig. 2).

The temperature and the salinity in the initial field are derived from the World Ocean Atlas (WOA2009) data in December with a spatial resolution of 1°×1° and 24 vertical layers (http:// www.nodc.noaa.gov/OC5/WOA09/netcdf_data.html). Meanwhile, u, v and zeta are set as 0.

The biogeochemical model is linked to the physical model with the same spatial and temporal resolutions. It is a representation of the pelagic nitrogen cycle and contains 12 compartments, including phytoplankton, chlorophyll a (Chl a), NO₃, NH₄, zooplankton, large detritus nitrogen, small detritus nitrogen, large detritus carbon, small detritus carbon, total inorganic carbon (TIC), TA, and DO (Fig. 3). Considering the biological characteristics in the east of China’s seas, we mainly focus on the modifications of the biological process (Ji et al., 2015), and optimized controlling equations and biological parameters have been shown in Ji et al. (2015). The other details of the model formulations were described by Fennel et al. (2006).

Observation data in the ECS from 1993 to 1994 (Fig. 1) are used to compare with the modeled results. Aside from the measurements of the temperature and the salinity, discrete water samples were collected for determination of DO, TA and NO₃. The station data at Sites 1, 2, 3, 4, 5 (ST-1, ST-2, ST-3, ST-4, ST-5) shown in Fig. 1a are from the survey cruises by Japan scientists from September to October in 1993. The observation data shown in Fig. 1b are derived from the survey cruises through the joint global ocean flux study in October 1993(JGOFS-1), April 1994 (JGOFS-2) and October 1994 (JGOFS-3), which is described in detail by Qiao et al. (2005). The JGOFS is an international and multi disciplinary programme with participants from more than 20 nations. Nine cruises of “margin flux in the East China Sea” project in East China Sea were carried out over the period from October 1993 to July 1998 (http://ijgofs.whoi.edu/). The ship of Venus is used for the JGOFS-1 survey cruise in October 1993. The ship of Kexue 1 is used for the JGOFS-2 survey cruise in April 1993, and Dongfanghong 2 is used for the JGOFS-3 survey cruise in Ocotber 1994. During the survey cruises, temperature and salinity were measured in the field with a conductivity, temperature and depth (CTD) detector. DO was measured using an iodine stoichiometry titration method. Nitrate was measured using a zinc cadmium reduction method.

The variation of the partial pressure of carbon dioxide in sea water is simultaneously affected or controlled by multiple factors. First, we evaluated the model performance by directly comparing the model results with the observations. Figure 4 shows the modeled temperature, salinity, DO, NO₃ and TA profiles above 1 000 and 100 m depth of water in April 1994 (Fig. 4b) and above 1 000 and 200 m depth of water in October 1993 (Fig. 4a), respectively. The corresponding profiles of the observations are also shown in Fig. 4. Generally, the modeled results have good agreement with observation results. As shown in Fig. 4, the mean errors between the modeled temperature and the observed data above 100 m in April and above 200 m in October are 0.60°C and 0.63°C, respectively, which means that high resolution modeled results could capture the distribution characteristics of thermocline. Meanwhile, the value of ROMS-NPZD modeled salinity falls within the range of the observations. The mean errors of the salinity between the observed and modeled salinities in April and October are 0.20 and 0.12, respectively. However, the largest deviation for the salinity reaches at 0.8 on the surface in April 1994 (Fig. 4b). The main reason for this deviation in surface is the air fluxes, such as precipitation and evaporation. But the deviation is small in other depths. Hence, the vertical variability of the modeled temperature and salinity exhibits similar features to the observations. In addition, the high resolution model reproduces the observed DO, NO₃ and TA concentration profiles reasonably well, but the predicted NO₃ concentrations are higher on the surface than the observations in October which may be resulted from the higher upward NO₃ flux from vertical upwelling (Fig. 4). The deviation range for TA at the upper 200 m level is from 5 to 35 mmol/m³. The reason for this deviation may be the biological model cannot perform the carbon transport well. But the deviation is less than the modeled results from Liu et al. (2009). Overall, the general good agreement between the model and the observations indicates that the model captures the characterized response to the internal biological processes and external forcing reasonably well. The validated model provides a solid basis for the mechanism analysis of the carbon cycle.

For further validation, Fig. 5 shows the linear regressions of the temperature, the salinity, DO and NO₃ between the modeled results and the observations from Japan and JGOFS-2 shown in Fig. 1. We only compare the observations and the model results for the upper 1 000 m. The linear regression slopes for the temperature, the salinity, DO and NO₃ concentrations are 0.94, 0.94, 0.89 and 0.95, respectively. Meanwhile, the high R-square values are obtained for all four variables, 0.95 for the temperature, 0.91 for the salinity, 0.88 for DO, and 0.95 for NO₃, which indicates that the model is capable of reproducing the absolute values for both the physical variables and biological variables.

As shown in Fig. 4, the profile comparison between the modeled results and the observations is not good enough in the upper 100 m, especially the NO₃. However, the biology activity in the euphotic zone has an important influence on the carbon cycle. Hence, the observation data collected by the ship in October 1993, April 1994 and October 1994 are used. There are 26 stations for the JGOFS-1, 68 stations for the JGOFS-2 and 38 stations for the JGOFS-3 (Fig. 1b). Meanwhile, the numbers of effective sample are listed in Table 1. On the basis of these data, the ME and MAE of the temperature, the salinity, DO, NO₃ and Chl a between the observations and the modeled results in the upper 100 m are analyzed.

For the upper 100 m depth, the averaged ME value is –0.19°C, 0.28, –7.51 mmol/m³, 1.81 mmol/m³ and 0.06 mg/m³ for the temperature, salinity, DO, NO₃ and Chl a, respectively. According to ME value shown in Figs 6a-e), the concentration of the modeled salinity, NO₃ and Chl a is higher than that from the observations in the upper 100 m, while the concentration of the modeled DO is lower than that of the observed DO. For the temperature, the modeled results are higher than observed results from 0 to 30 m, while lower in 50 and 100 m.

Meanwhile, for the upper 100 m depth, the averaged MAE value is 1.37°C, 0.50, 12.11 mmol/m³, 2.35 mmol/m³ and 0.29 mg/m³ for the temperature, salinity, DO, NO₃ and Chl a. As shown in Fig. 6f, the maximum MAE value of the temperature is 2.01°C at 100 m depth, and the minimum value is 0.99°C at 10 m depth. For the salinity shown in Fig. 6g, the maximum MAE value is 0.86 on the surface, and the minimum value is 0.23 at 100 m depth, which shows a decreasing trend with depth. However, for DO (Fig. 6h), the maximum MAE value is 16.61 mmol/m³ at 30 m depth, and the minimum value is 9.14 mmol/m³ at 100 m depth. For NO₃ shown in Fig. 6i, the maximum MAE value is 2.72 mmol/m³ at 50 m depth, and the MAE values at other depth are higher than 2 mmol/m³. The possible reason for this difference between the modeled NO₃ and the observed NO₃ is that the concentration of NO₃ in the ECS region in initial field derived from WOA09 is higher than the observation data; meanwhile, the concentration of NO₃ added in Changjiang River is another reason. Owing to the higher concentration of NO₃ in the model, the concentration of Chl a from the model is also higher than that from the observation data (Fig. 6j). The maximum MAE is 0.36 mmol/m³ at 30 m depth.

The main purpose of this paper is to study the variation characteristics of the partial pressure of carbon dioxide in sea water and the air-sea CO₂ flux. The conclusion that biological activity has an obvious influence on the distribution of the partial pressure of carbon dioxide in sea water and the air-sea CO₂ flux has been proposed by Chai et al. (2009). Hence, in order to validate the model’s performance on the biological activity, we undertake a comparison experiment between the modeled Chl a and the observed Chl a from the SeaWiFS from 1997 to 2005, whose results are shown in Fig. 7. On the basis of the satellite data (Fig. 7, blue line), the concentration of Chl a has a double-peak structure in 1 a, the maximum value is in spring and the second-maximum value is in autumn. The modeled Chl a has the same seasonal variation characteristic, and the monthly variation from the model is similar to the results from Hu et al. (2004), Liu and Yin (2007) and Zheng et al. (2012). The concentration of the modeled Chl a is less than that of the observed Chl a, especially in winter. The concentration of Chl a in the south of the Yellow Sea in winter is in a range of 0.3–0.6 mg/m³ simulated by Hu et al. (2004) using POM model, and is in a range of 0.2-0.6 mg/m³ in the Bohai Sea in winter simulated by Liu and Yin (2007). Hence, the concentration of Chl a from satellite in winter is a bit higher than that from in situ data. The main reason for this deviation is the uncertainty of the satellite data, especially in the near shore region. The calculation method for the concentration of Chl a from the SeaWiFS is based on Case I water (Wang and Shi, 2005; Wang et al., 2007). However the property of the study area belongs to Case II water, the ocean color would be affected by the concentration of Chl a, suspended matter and yellow substance. Hence, the absolute concentration of Chl a would be overestimated by the calculation method of Case I water.

The modeled climatological partial pressure of carbon dioxide in sea water shows strong seasonal variations (Fig. 8). In February, from north to south, the partial pressure of carbon dioxide in sea water increases with the decrease of latitude from 250 μatm in the north to 370 μatm in the south (Fig. 8a). The areas with being less than 250 μatm value are located in the Bohai Sea, Yellow Sea and the northern ECS, while areas with higher value (>350 μatm) are located in the southern ECS. Owing to the warm water and high nutrient concentration from the Kuroshio, the partial pressure of carbon dioxide in sea water is higher than 350 μatm in the path of the Kuroshio, especially in the east of Taiwan Province. In May, as shown in Fig. 8b, the partial pressure of carbon dioxide in sea water has a prominent increase with a maximum increasing gradient of 250 μatm. In August (Fig. 8c), the partial pressure of carbon dioxide in sea water reaches the peak value comparing with the other three months in the east of China’s seas. Because of the nutrients supplement from the Changjiang Diluted Water, a higher value (~600 μatm) appears in the Changjiang Estuary compared with the adjacent ocean areas. Meanwhile, under the function of upwelling, the partial pressure of carbon dioxide in sea water in the west of the Yellow Sea is higher than that in the center. Since the lowest partial pressure of carbon dioxide in sea water in August is above 400 μatm, which is still higher than that of the atmosphere, the CO₂ flux is from the sea to the air for the entire region of the east of China’s seas. In November (Fig. 8d), the value of the partial pressure of carbon dioxide in sea water has an obvious decrease, but it is still higher than that in February. The partial pressure of carbon dioxide in sea water is lower than 360 μatm in most areas where it performs as the sink of CO₂ to the atmosphere. Overall, the climatological monthly spatial partial pressure of carbon dioxide in sea water distribution in the east of China’s seas varies geographically.

The air-sea CO₂ flux is averaged over the entire east of China’s seas and evaluated from 1982 to 2005 (Fig. 9). As shown in Fig. 9, the air-sea CO₂ flux presents a prominent seasonal variation. The east of China’s seas domain-averaged monthly CO₂ flux from air-sea varies from –1.41 to 4.38 mol/(m²·a) with the lowest value in summer and highest value in winter. The east of China’s seas acts as a source of CO₂ to the atmosphere from June to October. The monthly minimum value of the air-sea CO₂ flux in August ranges from –2.09 to –0.44 mol/(m²·a), with the minimum value in August 1997 and the largest value in 1988, which indicates the positive SST anomaly favors the increase of the partial pressure of carbon dioxide in sea water in surface water and reduction of the CO₂ flux. In other months, the east of China’s seas serves as the sink of CO₂ to the atmosphere, which reaches the maximum value in January from 3.14 to 5.60 mol/(m²·a).

The annual mean air-sea CO₂ flux varies from 0.47 to 1.45 mol/(m²·a) from 1982 to 2005. The mean CO₂ of the 24 years flux predicted by the ROMS-NPZD model is about 1.06 mol/(m²·a) averaged from the entire east of China’s seas, which is equivalent to a regional total carbon of 3.22 Tg/a from the atmosphere to the ocean. However, the modeled result is smaller than the result (1.9 mol/(m²·a)) suggested by Tseng et al. (2013), but is larger than the result (0.87 mol/(m²·a)) suggested by Shim et al. (2007). Both the modeled and observed partial pressure of carbon dioxide in sea water show that the east of China’s seas is a sink for the atmospheric CO₂.

Figure 10 shows the interannual variation of the CO₂ flux and the Niño3 SST Index. The Niño3 SST Index measures the deviation from the normal SST in the eastern Pacific (5°S–5°N, 150°–90°W) (http://www.esrl.noaa.gov/psd/gcos_wgsp/Timeseries/Data/nino3.long.data). There is a clear inverse relationship between the Niño3 SST Index and the air-sea CO₂ flux. During the El Niño event, the CO₂ flux reduces obviously, especially in 1997. This is primarily due to the increase in the SST in the western Pacific, which results in the increase of the partial pressure of carbon dioxide in sea water in the ocean (Feely et al., 2002; Takahashi et al., 2003, 2009). Thus, the CO₂ flux in the east of China’s seas is connected with the ENSO events.

After removing the seasonal variation, the long-term time-series of the partial pressure of carbon dioxide in sea water and pH in the east of China’s seas show pronounced interannual variations over time from 1982 to 2005 (Fig. 11). As shown in Fig. 11, the time series of the ${p_{{\rm{C}}{{\rm{O}}_2}{\rm{sea}}}}$ anomaly ranges from –20 to 60 μatm, and Chai et al. (2009) estimated that the anomaly partial pressure of carbon dioxide in sea water in SCS is from –25 to 30 μatm. The partial pressure of carbon dioxide in sea water in the east of China’s seas from the linear regression slopes is 1.15 μatm/a, while the estimated increasing rate in north Pacific is between 0.5 and 2.0 μatm/a, and is estimated at (1.3±0.6) μatm/a in the center and west Pacific Ocean (Takahashi et al., 2009). Hence, modeled increasing rates of the partial pressure of carbon dioxide in sea water are within the range of others’ variability. Meanwhile, the ${p_{{\rm{C}}{{\rm{O}}_2}{\rm{air}}}}$ is increasing at a rate of 1.5 μatm/a in the central equatorial and subtropical northern Pacific Ocean due to anthropogenic emissions (Takahashi et al., 2003); the partial pressure of carbon dioxide in air of the east of China’s seas waters follows a consistent rate of increase, which leads to the increase of acidity in the sea. The growth rates of the partial pressure of carbon dioxide in sea water and partial pressure of carbon dioxide in air agree well with each other indicating the uptake of anthropogenic CO₂ as the major cause for long-term increases in DIC and decreases in CaCO₃ saturation state.

The year-to-year variation of pH is in a range of –0.06–0.02, and the reducing rate is 0.001 3 a^–1 which reveals the ocean acidification characteristic. According to the observation data, the averaged ocean surface water pH has fallen from approximately 8.21 to 8.10 by approximately 0.1 units since preindustrial times (IPCC, 2000), and is expected to decrease a further 0.3–0.4 pH units (Orr et al., 2005) if atmospheric CO₂ concentration reaches 800 μatm. Solomon (2007) also estimates the reducing rate is 0.002 a^–1 for pH in the North Atlantic seas. The modeled pH decreasing rate is smaller than others. This discrepancy could be resulted from the fact that the time series observational data are obtained from a long-term observation in the Atlantic sea, while the modeled time is much shorter in the east of China’s seas.

Surface variables (the partial pressure of carbon dioxide in sea water, the SST and the Chl a concentration) are examined to the seasonal variation over the entire east of China’s seas (Fig. 12). Domain-averaged monthly partial pressure of carbon dioxide in sea water varies between 280 and 430 μatm with the highest value in August and the lowest value in January. According to the value of ${p_{{\rm{C}}{{\rm{O}}_2}{\rm{air}}}}$ 373 μatm, averaged from 1990 to 2004 (Chai et al., 2009), hence the east of China’s seas is a sink of CO₂ to the atmosphere in winter, early spring and later autumn, and a source in the other times of the year.

In the east of China’s seas the domain-averaged monthly SST is in a range of 14–28°C. The SST has the same variation tendency with the partial pressure of carbon dioxide in sea water, which reaches the highest value of 28°C in August and the lowest value of 14°C in January. As the trend line shown in Fig. 12a, the partial pressure of carbon dioxide in sea water has a positive correlation with the SST, which means the seasonal variation of ${p_{{\rm{C}}{{\rm{O}}_2}{\rm{sea}}}}$ is controlled by the SST.

The range of Chl a concentration is from 0.1 to 0.7 mg/m³ with the highest value of 0.7 mg/m³ in March and the lowest value of 0.1 mg/m³ in August (Fig. 12b). Owing to the strong light intensity, warm sea water and plenty of nutrients accumulated in winter, the phytoplankton reproduces rapidly in most areas of the China’s seas. It also can be found that the seasonal variation of Chl a concentration has an opposite tendency with the partial pressure of carbon dioxide in sea water, which means phytoplankton is another control factor of the partial pressure of carbon dioxide in sea water. During the growth of phytoplankton, CO₃^2– would be consumed by biological activity as a kind of nutrients; hence the partial pressure of carbon dioxide in sea water is lower in this process (Jin and Shi, 2001; Liu et al., 2002; Chai et al., 2009).

The in-phase relationship between the partial pressure of carbon dioxide in sea water and the SST and out-of-phase relationship between the partial pressure of carbon dioxide in sea water and Chl a concentration suggest that the partial pressure of carbon dioxide in sea water is regulated by both the SST and the biological activity in the east of China’s seas.

It has been estimated that the oceanic uptake and release of CO₂ are governed by the dynamic equilibrium of the sea temperature, the biological utilization of CO₂, and the upwelling flux of subsurface waters with high CO₂ concentration (Feely et al., 2001; Takahashi et al., 2002). In order to isolate the effect of each factor on the partial pressure of carbon dioxide in sea water in the east of China’s seas, a series of sensitivity experiments on basin-wide SST, SSS, TIC, and TA are conducted; one factor is set as a constant each time and assigned with its annual mean value. The standard experiment is based on the seasonal cycle of the monthly averaged SST, SSS, TIC and TA in the east of China’s seas.

As shown in Fig. 13, the seasonal variation of the partial pressure of carbon dioxide in sea water varies from 280 to 430 μatm in the standard experiment, which is low in winter and high in summer. When the SST value is fixed as annual mean, the partial pressure of carbon dioxide in sea water has a pronounced change compared with the standard value. Since the annual mean value of the SST is higher in winter and lower in summer than that in the standard experiment, the seasonal amplitude of the partial pressure of carbon dioxide in sea water is from 310 to 390 μatm, and is higher in winter and lower in summer. Obviously, the seasonal cycle of the partial pressure of carbon dioxide in sea water responds to the SST changes, which also means that the SST has a strong effect on the partial pressure of carbon dioxide in sea water. When fixed the SSS and TA, both the tendency and value of the partial pressure of carbon dioxide in sea water have little changes compared with the value in the standard experiment, which means that the SSS and TA have less influence on the partial pressure of carbon dioxide in sea water. With fixed TIC, the partial pressure of carbon dioxide in the sea water has the same changing trend with that in the standard experiment, but the value has a large variation which ranges from 250 to 480 μatm. Hence, TIC has a strong effect on the partial pressure of carbon dioxide in sea water in the east of China’s seas.

The amplitudes of the partial pressure of carbon dioxide in sea water annual variation (Δ ${p_{{\rm{C}}{{\rm{O}}_2}{\rm{sea}}}}$ =${p_{{\rm{C}}{{\rm{O}}_2}{\rm{sea,\,max}}}}$ =–${p_{{\rm{C}}{{\rm{O}}_2}{\rm{sea, \,min}}}}$ are 134 μatm for the standard experiment, and 69, 142, 114 and 215 μatm in the experiments with annual mean of SST, SSS, TA and TIC, respectively. The amplitude of the increment of Δ${p_{{\rm{C}}{{\rm{O}}_2}{\rm{sea}}}}$ decreases by 65 μatm under the condition of fixed SST, but it increases by 81 μatm when the TIC is set as its annual mean value. It is only a slightly change in values of 8 and 20 μatm when fixed SSS and TA.

In order to analyze the main control factor of the partial pressure of carbon dioxide in sea water in the east of China’s seas, the method given by Takahashi et al. (2002) is used. The formulation is as follows: T/B=Δp_T(CO₂)/Δp_B(CO₂), T-B=Δp_T-(CO₂)-Δp_B(CO₂), where T refers to the temperature effect on the partial pressure of carbon dioxide in sea water, and B is the biological activity effect, hence, the relative rate of the temperature effect to the biological carbon utilization is T/B=65/81=0.80, and T-B=–16 μatm. Therefore, the influence of biological activity is greater than that of temperature in the east of China’s seas, which is consistent with the conclusion in the north of 40°N in the northern Pacific estimated by Takahashi et al. (2002). Gypens et al. (2004) also pointed out that biological activity has stronger influence on the partial pressure of carbon dioxide in sea water than the SST in the southern bight of the North Sea.