1 Introduction

The equatorial Pacific is the major source region for outgassing CO2 to the atmosphere, annually amounting to 0.44 ± 0.14 PgC (Feely et al. 1999; Ishii et al. 2014). In this region, CO2 exhibits multiple variability from interannual to interdecadal timescales. On interannual timescale, El Niño-Southern Oscillation (ENSO) influences strengths of trade winds and upwelling in the central and eastern equatorial Pacific, and further affects marine primary production and carbon cycle (Landschützer et al. 2014; Zhang and Gao 2016; Kang et al. 2017). Previous studies (e.g. Feely et al. 1999, 2006; Rayner et al. 1999; Le Quéré et al. 2000; Wanninkhof et al. 2013) have demonstrated that interannual variability of CO2 fluxes in this region accounts for 70% of that in the global ocean. On decadal timescales, major physical and biological changes are evident over the Pacific basin. An example for this fluctuation is commonly called as the interdecadal Pacific Oscillation (IPO) in the climate community (Power et al. 1999; Newman et al. 2003; Liu 2012; Meehl et al. 2016). The IPO experienced two pronounced regime shifts in 1975–1977 and 1997–1998, which is clearly represented in anomalies of sea surface temperature, wind stress and even fish production (e.g. Mantua et al. 1997). For instance, the negative (cooling) phase of the IPO after 1999 is associated with a cooling trend in the eastern tropical Pacific that has contributed to recent global warming hiatus (Kosaka and Xie 2013; England et al. 2014). Although the cause and influence of the IPO have been widely investigated and understood qualitatively (e.g. Trenberth and Hurrell 1994; Power et al. 1999; Zhang et al. 1999; Choi et al. 2012; Han et al. 2014; Chen and Tung 2018; Tung et al. 2019), large uncertainties exist in the magnitudes of interdecadal variations in CO2 fluxes owing to the limitation of observed data and model developments (e.g. Patra et al. 2005; Wetzel et al. 2005; Feely et al. 2006; Doney et al. 2009; Ishii et al. 2009, 2014; Wanninkhof et al. 2013; Fay and McKinley 2013; Valsala et al. 2014; Xiu and Chai 2014; Dunne et al. 2015; McKinley et al. 2017).

In addition to the uncertainty in the variability of CO2 fluxes, the mechanisms affecting interdecadal variability of CO2 fluxes are still not understood well. The CO2 fluxes at the air–sea interface are determined by several factors, including the pCO2 difference (ΔpCO2, pCO2 at the sea surface minus pCO2 in the atmosphere), wind speed, temperature and salinity (Wanninkhof et al. 2009). In addition, the sign of CO2 fluxes between ocean and atmosphere is determined by ΔpCO2. Because the spatio-temporal variability of atmospheric CO2 is relatively small, the variability of ΔpCO2 reflects mainly in the sea surface pCO2. In quantifying oceanic role, the decadal variability of sea surface pCO2 was also investigated by several modelling studies (Valsala et al. 2014; Wang et al. 2015). Model results demonstrated that ocean dynamics induced change in dissolved inorganic carbon (DIC) plays a key role in determining the decadal variability of pCO2. For instance, Valsala et al. (2014) found that decadal change in DIC can be traced to the North Pacific through thermocline pathway. By using a biogeochemical model, Wang et al. (2015) demonstrated that the equatorial Pacific is a DIC-driven system of carbon cycle on decadal timescale, but the mechanism for controlling carbon system variability on interdecadal timescale has not been investigated adequately.

The CO2 fluxes are also strongly influenced by wind speed in addition to ΔpCO2, and the contributions from temperature and salinity to CO2 fluxes are relatively small. This is because the products of gas transfer velocity and solubility, the factors affecting CO2 fluxes, have weak dependence on temperature (Wanninkhof and Triñanes 2017). On interdecadal timescale, the IPO plays a significant role in affecting the Walker Circulation in the Pacific. For example, during the recent decade of this century, the unprecedented intensification of trade winds associated with the cooling phase of the IPO is anticipated to affect the CO2 fluxes in the Pacific through the variability of wind speed (England et al. 2014; Bordbar et al. 2017). Wanninkhof and Triñanes (2017) found that the increasing of wind speed led to an increase in efflux of CO2 in the equatorial Pacific by 0.03–0.04 PgC decade−1 during 1988–2014. Subsequently, the net CO2 uptake of global ocean slightly decreases by 0.00–0.02 PgC decade−1. Feely et al. (2006) suggested that the increased CO2 fluxes were due to the increase in wind speeds after the spring of 1998 when regime of the IPO shifted from positive (warm) phase to negative (cold) phase. However, the relative contributions of wind speed and ΔpCO2 to the interdecadal variability of CO2 fluxes have not been quantified. Moreover, due to quadratic dependence of CO2 fluxes (FCO2) on wind speed (u) (\(FCO_{2} \propto u^{2}\)), the increased frequency of La Niña events during the IPO cold phase may lead to an increase in wind speed and further an increase in CO2 fluxes on interdecadal timescale. This study will mainly focus on these issues.

Previous studies have focused more on the recent regime shift during 1997–1998, but less on the earlier regime shift during 1975–1977. In addition, the magnitude of the interdecadal variability of CO2 fluxes and the underlying mechanism are not clear. The observational data of CO2 fluxes are only available from 1970s; relatively short time series may not be sufficient to depict the regime shift of CO2 fluxes on decadal timescale. The biogeochemical modeling is an alternative way to study interdecadal variability of air–sea CO2 fluxes and its relationships with climatic variability like the IPO. In this study, we investigate the interdecadal variability of CO2 fluxes and possible mechanisms responsible for it, using a fully coupled ocean physics–biogeochemical model forced by NCEP/NCAR winds during 1948–2016.

The paper is organized as follows. Section 2 describes the model setup and dataset used for validation. Section 3 examines the interdecadal variability of CO2 fluxes and the roles played by wind and ΔpCO2 in the variability. A discussion is given in Sect. 4, and a summary is presented in Sect. 5.

2 Model description and data used

2.1 Ocean general circulation model

The ocean general circulation model (OGCM) used in this study is a primitive equation model (sigma-coordinate, reduced-gravity), specificially developed for the upper equatorial ocean (Gent and Cane 1989). An advective atmosphere mixed layer model for calculating sea surface heat fluxes (Seager et al. 1995; Murtugudde et al. 1996) is coupled with the OGCM. The model domain covers the entire tropical Pacific basin (120°E–76°W, 30°S–30°N). The model has 20 vertical layers with variable thicknesses; a mixed layer at the top is determined by a mixed layer model (Chen et al. 1994). The zonal resolution of this model is 1° in the central basin and gradually increases to 0.4° in the western and eastern boundaries. The meridional resolution is from 0.3° to 0.6° between 15°S and 15°N and gradually decreases to 2° at the northern and southern boundaries. Sponge layers are set within the 10° domain near the northern and southern boundaries. Some physical and biological variables (e.g. temperature, salinity, and nitrate) are gradually relaxed back to their corresponding climatological fields from WOA98 atlas (http://www.nodc.noaa.gov/OC5/indprod.html).

The model is initialized by temperature and salinity from the World Ocean Atlas data (WOA01) and spun up for 30 years under atmospheric climatological forcing. Subsequently, the model is integrated from 1948 to 2016, forced by daily wind fields from the National Centers for Environmental Prediction/National Center for Atmospheric Research (NCEP/NCAR) reanalysis (Kalnay et al. 1996), and the climatological fields of solar radiation, clouds and precipitation. The monthly output during the period of 1958–2016 is used for our analyses.

2.2 A carbon chemistry model

The biogeochemical model consists of 12 components, including six biological components [large (L) and small (S) size classes of phytoplankton (P), zooplankton (z) and detritus (D)] and six kinds of nutrients (nitrate, ammonium, dissolved oxygen, silicon, dissolved inorganic carbon (DIC), and dissolved iron). The model equations and structure were detailed by Wang et al. (2008). The vertical mixing parametrization schemes for all biological components are similar to those for temperature and salinity at each layers (Chen et al. 1994), with unified units being used by mol N m−3.

The carbon chemistry model embedded in the ocean physical model had been described in Wang et al. (2006, 2015). Briefly, CO2 fluxes (FCO2) from sea surface into the atmosphere are calculated as follows;

$$FCO_{2} = SK_{0} \Delta pCO_{2}$$
(1)

where S is the solubility of CO2 calculated from temperature and salinity; K0 is the gas transfer velocity (Wanninkhof 1992)

$$K_{0} = 0.31u^{2} \left( {\frac{Sc}{{Sc{}_{20}}}} \right)^{{ - \frac{1}{2}}}$$
(2)

where u is wind speed from the NCEP/NCAR reanalysis and Sc is the Schmidt number; ΔpCO2 represents the difference in pCO2 between sea surface and the atmosphere. The atmospheric pCO2 data are taken from http://aftp.cmdl.noaa.gov/products/trends/CO2/CO2_annmean_mlo.txt during 1948–2016. The alkalinity is calculated based on the salinity–alkalinity relationship derived from the Pacific GLODAP bottle data (http://cdiac.ornl.gov/oceans/glodap/).

2.3 Coupling between physics and biogeochemistry in the model

Recently, we updated the model to investigate the interaction between ocean physics and biogeochemistry in the tropical Pacific (Zhang et al. 2018a, b). A parameterization scheme is introduced to represent chlorophyll induced heating effect on the upper ocean (Wang et al. 2008; Zhang 2015), which is allowed to affect ocean thermodynamics and further change in the biogeochemical condition. Therefore, this new model adopts a two-way coupling strategy between physical and biogeochemical processes. As a result, this coupling allows for bio-feedback onto temperature, stratification, and mixing (Zhang et al. 2018a), which can further affect the solubility of pCO2 in the seawater (solubility pump) and ocean stratification.

2.4 Data

Monthly sea surface temperature data are taken from Extended Reconstructed Sea Surface Temperature, Version 5 (ERSSTv5) over the period of 1958–2016 (Huang et al. 2017). Annual mean CO2 fluxes data is from Global Surface pCO2 Database V2016 at Lamont–Doherty Earth Observatory (LDEO), Columbia University (Takahashi et al. 2009). Besides, an updated observation-based global monthly gridded air–sea CO2 fluxes product (Landschützer et al. 2016) is used to validate the model simulations. This pCO2 product is based on a two-step neural network approach to extrapolate the monthly gridded SOCAT v4 product (Bakker et al. 2016). Next, sea–air CO2 flux maps are computed using a standard bulk formulation and high-resolution wind speeds, with the spatial resolution of 1° × 1° and time range being from 1982 to 2015.

3 Results

3.1 Model validation

We first use the Annual Flux Gridded Database (Takahashi et al. 2009) to validate annual mean CO2 fluxes in the model simulation. As displayed in Fig. 1a, b, the model captures the spatial pattern of annual mean CO2 fluxes quite well in the equatorial Pacific. Positive values indicate that ocean release CO2 to the atmosphere. For the observation, regions with large CO2 fluxes are seen in the southeastern tropical Pacific and those with low values are seen in the western equatorial and subtropical Pacific. These observed features are faithfully captured by the model, although the simulated annual mean CO2 fluxes are slightly higher than observation in the southeastern tropical Pacific (Fig. 1b). This model bias may be related to strong upwelling represented in the ocean model simulation.

Fig. 1
figure 1

Annual mean of sea-air CO2 fluxes during 1995–2005 from Takahashi et al. (2009) database (a), and from model results (b). c Niño3.4 SST anomalies from ERSST-V5 (black line) and model results (red line) during the period of 1958-2016. The positive value denotes the oceanic releases of CO2 to the atmosphere and negative value denotes the oceanic absorption of CO2. The contour interval is 1 mol C m−2 year−1 in a and b

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To evaluate the model performance in simulating interannual to interdecadal variability of SST in the tropical Pacific, we compared the simulated SST with that in ERSST-v5 through calculating detrended Niño3.4 index from 1958 to 2016 (Fig. 1c). The model can well reproduce the main ENSO events (e.g. 1997–1998 El Niño event). The correlation coefficient reaches 0.80 between modeled and observed Niño3.4 index, indicating that model outputs can be used to investigate interannual to interdecadal variability in the tropical Pacific.

Furthermore, we examined the decadal variability of CO2 fluxes by comparing the simulated decadal mean CO2 fluxes to observation from Ishii et al. (2014) during the periods of 1990–1999 and 2000–2009. The data in Ishii et al. (2014) are obtained from various approaches (observation-based and biogeochemical model products) (Table 1). The decadal mean values of air–sea CO2 fluxes simulated by the model are 0.41 ± 0.14 PgC year−1 during 1990–1999 and 0.53 ± 0.16 PgC year−1 during 2000–2009, respectively. This decadal change in CO2 fluxes is associated with the phase change in the IPO, and is in good agreement with the observation-based estimate (+ 0.49 ± 0.07 PgC year−1 and + 0.56 ± 0.11 PgC year−1, respectively). In addition, as shown in Fig. 2, we compared the tropical Pacific CO2 fluxes from model output with an observation-based global monthly gridded product for air–sea CO2 fluxes (Landschützer et al. 2016) during 1982–2015. Figure 2 shows that seasonal to decadal variabilities of CO2 fluxes are well-correlated (correlation coefficient of 0.57) between observation-based product and model output in the entire tropical Pacific (120°E–80°W, 18°S–18°N) (Fig. 2a). Meanwhile, the correlation coefficients are 0.46 and 0.91 in the Niño3 region (150°W–90°W, 5°S–5°N) and Niño4 region (160°E–150°W, 5°S–5°N), indicating that model can well capture the variability of CO2 fluxes in the tropical Pacific, especially in the western-central equatorial Pacific (Fig. 2b, c).

Table 1 Decadal mean values of air–sea CO2 fluxes in the equatorial Pacific (18°S–18°N) from various studies calculated during two periods (1990–1999, 2000–2009). (Units: PgC year−1)
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Fig. 2
figure 2

Comparisons of integrated CO2 fluxes between model and observation-based air–sea CO2 flux product (Landschützer et al. 2016) for a in the entire tropical Pacific (120°E–80°W, 18°S–18°N), (b) the Niño3 region (150°W–90°W, 5°S–5°N), and c the Niño4 region (160°E–150°W, 5°S–5°N). The corresponding correlation coefficients are given

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3.2 Interdecadal variability of CO2 fluxes: two regime shifts

Figure 3a shows that CO2 fluxes in the equatorial Pacific experienced two pronounced decadal shifts during the period 1958–2016. The first one occurred in 1975–1976 when the IPO shifted from cold phase (1958–1975) to warm phase (1976–1997). This period was characterized by a decrease in CO2 fluxes nearly by 0.4 mol C m−2 year−1 during the period of 1976–1997. During this period, the slowdown of shallow meridional overturning circulation lead to surface warming by 1 °C (Zhang and Levitus 1997; McPhaden and Zhang 2002) and a decrease in DIC by 5–10 mmol m−3 (Fig. 3c). In addition, El Niño events occur frequently during this positive IPO phase, and lead to a decrease in wind speed by 1–2 m s−1 (Fig. 4). As shown in Fig. 4a, central Pacific (CP) El Niño type occurred frequently during recent decades, which is characterized by positive SST anomaly being concerntrated in the central equatorial Pacific (e.g. Ashok and Yamagata 2009; Kug et al. 2009; Yu and Kim 2010). Consequently, large interannual anomaly center of wind speed tends to be located near the dateline (Fig. 4b). The decrease in wind speed can reduce the outgassing of CO2 from sea surface during El Niño events (Figs. 4b, 5b). Subsequently, the maximum variability region of CO2 flux migrates westward gradually during this period (Fig. 5b). Meanwhile, the regime shift of ΔpCO2 is similar to that of DIC, suggesting that interdecadal phase change of DIC has an important influence on that of ΔpCO2 (Figs. 3b, c, 5a).

Fig. 3
figure 3

The modeled detrended interannual anomalies of sea-to-air CO2 fluxes (a), sea surface pCO2 (b), DIC (c) and NCP (d) during the period of 1958–2016 in the tropical Pacific (120°E–80°W, 18°S–18°N). The black line denotes the 5-year running mean for interannual anomalies. Note the black dashed line in b is sea surface pCO2 at 25 °C. The units are mol C m−2 year−1 in a, ppm in b, mmol C m−3 in c and mmol C m−3 days−1 in d

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Fig. 4
figure 4

The interannual anomalies along the equator for SST (a) and wind speed from NCEP/NCAR reanalysis (b) during the period 1958–2016. The long-term trends are removed. The units are °C in a and m s−1 in b

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Fig. 5
figure 5

The interannual anomalies along the equator for ΔpCO2 (a) and CO2 fluxes (b) during the period 1958-2016. The long-term trends are removed. The units are ppm in a and mol C m−2 year−1 in b

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The second regime shift took place around 1997–1998. Recent similar studies showed that the outgassing fluxes of CO2 appeared to have a slight increase in the equatorial Pacific when the IPO regime shifted from warm phase (1976–1997) to cold phase (1998–2012) during 1997–1998 (Feely et al. 2006). Since 1998, the tropical Pacific trade winds strengthened again and wind-driven circulation spun up, with the surface cooling emerged in the central and eastern equatorial Pacific (Fig. 4a) (Kosaka and Xie 2013; England et al. 2014). The increase in trade winds led to an increase in CO2 fluxes during this IPO phase (Figs. 3a, 5b). Contrasts to the former cold phase of the IPO (1958–1975), large SST anomaly regions are confined more to the central Pacific during this IPO cold phase. This is because the frequencies of La Niña increase during the IPO cold phase, with the cold SST anomalies during La Niña tending to be more westward than positive SST anomalies during El Niño. Figures 4b and 5b show that positive anomalies of CO2 fluxes are associated with an increase in wind speed in the central Pacific during La Niña events (Fig. 4b). The increased frequency of La Niña further leads to an increase in CO2 fluxes through the amplifying effect of wind speed during this IPO cold phase. Because the frequencies of El Niño (La Niña) occurring can be modulated by background state (warming or cooling trend) of the tropical Pacific on interdecadal timescale (Lin et al. 2018; An 2018), the interdecadal variability of CO2 fluxes is tightly associated with ENSO frequency and asymmetry on interdecadal timescale. In addition, the increased La Niña events during the IPO cold phase further result in westward migration of maximum anomalies for CO2 fluxes. However, the interannual anomalies of ΔpCO2 are mainly located in the eastern Pacific (Fig. 5a), indicating that ΔpCO2 may have little influence on interannual variability of CO2 fluxes during this IPO phase.

Besides the physical factors, the biological activity also exhibits distinguished interdecadal fluctuations. Figure 3d shows that net community production (NCP) decreases in the warm phase but increases in the cold phase of the IPO, although the timing of regime shift slightly lags behind the other process like DIC by 1–2 years (e.g. the regime shift of NCP occurred in 2000–2001). The NCP represents the net change of DIC at the sea surface due to the biological uptake and regeneration (Wang et al. 2006). Therefore, the interdecadal variability of NCP can exert influence on seawater pCO2 by removing DIC in the mixed layer. The details of how NCP affects pCO2 will be explored further below.

3.3 Interdecadal changes in the relationships of CO2 fluxes with wind speed and ΔpCO2 anomalies

Because CO2 fluxes are mainly determined by wind speed and ΔpCO2, the interdecadal changes in the relationships between the CO2 fluxes and wind speed or ΔpCO2 can be further estimated by a regression analysis. According to the timing of regime shifts for CO2 fluxes (Fig. 3a), we divided the entire period (1958–2016) into three sub-periods, i.e. 1958–1975, 1976–1997, and 1998–2012. The recent period of 2013–2016 was not taken into account so that the influence of the extreme El Niño in 2015–2016 on the analysis results is excluded (Zhang and Gao 2016; Hu and Fedorov 2017). In addition, regression analysis is conducted in the Niño4 region (160°E–150°W, 5°S–5°N) and the Niño3 region (170°W–120°W, 5°S–5°N), respectively. As indicated in Fig. 6a, the regression coefficients between CO2 fluxes and wind speed are 0.57, 0.41, and 0.65 mol C m−2 year−1 per 1 m s−1 in the Niño4 region during the period of 1958–1975, 1976–1997, and 1998–2012, respectively. Thus, the regression coefficients exhibit clearly interdecadal fluctuations associated with the IPO phases. Given the same wind speed anomaly, the amplitude of variability in CO2 fluxes due to the wind speed anomalies can be increased during the IPO cold phase in the western-central equatorial Pacific, but decreased during the IPO warm phase.

Fig. 6
figure 6

Scatterplots for anomalies of the wind speed and of CO2 fluxes in the Niño4 (a) and Niño3 region (b), which are separately illustrated during the three periods (1958–1975, 1976–1997 and 1998–2012). c, d are similar to a, b but for those of the ΔpCO2 and CO2 fluxes

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In the eastern equatorial Pacific (Fig. 6b), the regression coefficients between CO2 fluxes and wind speed decrease unanimously during these periods and exhibit no interdecadal phase change (i.e. the regression coefficients are 1.4, 1.3 and 0.9 mol C m−2 year−1 per 1 m s−1 in the Niño3 region during the period 1958–1975, 1976–1997 and 1998–2012, respectively). Thus, the regression coefficients increase in the western-central Pacific, but decrease in the eastern Pacific during these three sub-periods. It is suggested that the possible influence of global warming tends to enhance (weaken) the relationship between CO2 fluxes and wind speed in the western-central (eastern) Pacific. Meanwhile, the annual mean values of CO2 fluxes during these three periods exhibit clear interdecadal shifts in the Niño4 region (1.40, 1.10, 1.56 mol C m2 year−1 during 1958–1975, 1976–1997 and 1998–2012). However, as indicated in the Niño3 region, the interdecadal shifts of CO2 fluxes are not clearly represented (2.89, 1.87, 1.76 mol C m2 year−1 during 1958–1975, 1976–1997 and 1998–2012) (Table 2).

Table 2 The mean values and standard deviations (trends) of various variables calculated during three different regimes (1958–1975, 1976–1997, and 1998–2012) and entire period (1958–2012)
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The similar regression analyses are conducted between ΔpCO2 and CO2 fluxes (Fig. 6c, d). Figure 6c shows that regression coefficients are 0.02, 0.02, and 0.03 mol C m−2 year−1 per ppm in the Niño4 region during the period 1958–1975, 1976–1997 and 1998–2012, respectively. This indicates the relatively weak influence of ΔpCO2 on the interdecadal shift of CO2 fluxes variability in the western-central Pacific. In the eastern equatorial Pacific, the amplitude of CO2 flux variability due to the ΔpCO2 anomalies is decreased from 1958 to 2012 (Fig. 6d), consistent with the change in the relationship between wind speed and CO2 fluxes. These results imply that anthropogenic forcing can further affect the relationship between factors determining the variability of CO2 fluxes (wind speed and pCO2) and itself in different regions. Next, the pronounced effect of wind speed on CO2 fluxes is further illustrated by using a diagnostic analysis in the following.

3.4 The effects of wind speed and ΔpCO2 on interdecadal variability of CO2 fluxes: A diagnostic analysis

Wind speed has a vital influence on the gas transfer velocity, which further affects the air–sea CO2 fluxes according to Eq. (2) (Wanninkhof and Triñanes 2017). In addition, the sign of CO2 fluxes is determined by ΔpCO2. To isolate the impacts of wind speed and ΔpCO2 on CO2 fluxes, analysis strategies are taken as follows:

  1. (1)

    According to Eq. (1), the total wind fields (with seasonal to interdecadal signals all included) derived from the NCEP/NCAR, and other variables (ΔpCO2, SST, SSS and DIC) derived from model output are used to calculate the CO2 fluxes. This case is referred to as Wind-inter, in which the effects of interannual variability of wind speed and ΔpCO2 are both included.

  2. (2)

    Then, the climatological field of wind speed is used to calculate the CO2 fluxes (i.e. interannual-varying wind speed derived from the NCEP reanalysis is not taken into account). Other fields (ΔpCO2, SST, SSS and DIC) are set the same as in Wind-inter. This case is referred to as Wind-clim, in which only seasonally varying wind speed is taken into account whereas interannual variability effect of ΔpCO2 is included.

  3. (3)

    Another analysis is conducted in which ΔpCO2 is set to its climatology derived from model output, but wind speed is prescribed to be interannually varying as in Wind-inter. This case is referred to as ΔpCO2-clim, i.e. interannual variability effect of ΔpCO2 is excluded, whereas interannual variability of wind speed is retained.

Due to the quadratic dependence of gas transfer velocity (K0) on wind speed (u) in Eq. 2, the interannual anomalies of wind speed directly amplify the interannual variability of K0. Therefore, the interdecadal variability of gas transfer velocity K0 (Eq. 2) can be directly linked to the frequency of El Niño and La Niña events during the IPO warm and cold phase. For example, during the IPO warm phase (1976–1997), El Niño events occur frequently (Fig. 4a), which leads to a decrease in wind speed in the central-eastern Pacific. Meanwhile, gas transfer velocity is assumed to be a quadratic dependency on wind speed (u2) as described in Eq (2) (i.e. CO2 fluxes ∝ u2), and so the effect of wind speed on CO2 fluxes can be amplified through this quadratic dependency on interdecadal scale. Thus, an increase in the number of El Niño events can lead to a decrease in u2, which subsequently leads to a decrease in CO2 fluxes during the IPO warm phase.

Figure 7a–c shows the interdecadal anomalies of CO2 fluxes derived from Wind-inter over three averaged periods (i.e. 1958–1975, 1976–1997, and 1998–2012). The maximum anomaly region of interdecadal CO2 fluxes is located in the southeastern tropical Pacific, reaching 0.2 mol C m−2 year−1 during 1958–1975. The mean outgassing flux of CO2 is 1.07 ± 0.19 mol C m−2 year−1 in the equatorial Pacific (18°S–18°N) during the period (Table 2), which is significantly higher than observational estimates during recent decades (Ishii et al., 2014). When the IPO phase becomes positive, the mean CO2 fluxes decrease to 0.68 ± 0.14 mol C m−2 year−1 and interdecadal anomalies of CO2 fluxes become negative in the entire equatorial Pacific during 1976–1997 (Table 2, Fig. 7b). In the recent period being so-called global warming “hiatus” (1998–2012), the rebound of overturning circulation may lead to an increase in the mean CO2 fluxes (0.76 ± 0.15 mol C m−2 year−1) (Table 2, Figs. 7c, 8a). It is noteworthy that the pattern of interdecadal anomalies of CO2 fluxes exhibits the possible interaction between the tropics and extratropics. The pattern of interdecadal anomalies in CO2 fluxes is similar to the paths of water parcels as suggested by Gu and Philander (1997) and Zhang et al. (1998).

Fig. 7
figure 7

The detrended interdecadal anomalies of CO2 fluxes during the period of 1958–1975 (a), 1976–1997 (b) and 1998–2012 (c), which are calculated using interannually varying wind (denoted as Wind-inter). The d–f and g–i are the same as in a–c but for the results derived using climatological winds (denoted as Wind-clim) and climatological ΔpCO2 (denoted as ΔpCO2-clim), respectively. The contour intervals are 0.1 mol C m−2 year−1

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In the Wind-clim case, the effect of interdecadal wind of variability is removed in the calculation of CO2 fluxes. The resultant amplitude of interdecadal variability in CO2 fluxes is significantly weakened in the western-central equatorial Pacific (Figs. 7d–f, 8c). The weakened interdecadal variability of CO2 fluxes in Wind-clim indicates that interdecadal variability of wind speed plays a dominant role in determining the amplitude and location of interdecadal variability of CO2 fluxes. In Fig. 7a–c, the region with maximum interdecadal anomalies of CO2 fluxes gradually migrates westward along the equator in Wind-inter, but this feature is not evident in Wind-clim. As shown in Fig. 4b, the region with large interannual and interdecadal variabilities of wind speed tends to be confined to the central equatorial Pacific. In Wind-clim, the effects of interannual and interdecadal variability of wind speed are excluded, so the interdecadal anomalies of CO2 fluxes are mainly due to the change in ΔpCO2. Figure 7d–f show that the impacts of ΔpCO2 on CO2 fluxes are mainly located in the northern tropical ocean and southeastern Pacific on interdecadal timescale, indicating that the effects of ΔpCO2 on CO2 fluxes come from the off-equatorial region.

Figure 7g–i show interdecadal anomalies of CO2 fluxes in the ΔpCO2-clim. In this case, the effect from interannual and interdecadal variability of ΔpCO2 is excluded. This result can be compared to that of Wind-inter in terms of the amplitude and location of interdecadal CO2 flux anomalies. In ΔpCO2-clim, the amplitudes of interdecadal variability in CO2 fluxes are slightly weakened in the western-central equatorial Pacific as indicated in Fig. 7g–i, indicating that the impact of wind speed dominates interdecadal variability of CO2 fluxes, whereas that of ΔpCO2 plays a secondary role in determining the interdecadal variability of CO2 fluxes. In addition, the interannual variability of wind speed is more important on that of CO2 fluxes in the central Pacific, while that of ΔpCO2 is important in the eastern Pacific and extratropics (Figs. 7d–f, 8b). Overall, wind speed plays a vital role in determining the interdecadal variability of CO2 fluxes, and the contribution from ΔpCO2 is relatively small.

3.5 Interdecadal variability of sea surface pCO2

The ΔpCO2 (surface water pCO2 minus atmospheric pCO2) is another major factor in determining the outgassing of CO2 into the atmosphere (Eq. 2), especially in terms of determining the sign of CO2 fluxes at the air–sea interface. Although the contribution of ΔpCO2 to CO2 fluxes is relatively small in the tropical Pacific (Fig. 8), the interdecadal change of ΔpCO2 is still evident in some regions (Figs. 3, 4). The interdecadal variability of ΔpCO2 and the mechanism responsible for it are analyzed in this section.

Fig. 8
figure 8

Mean fields of air–sea CO2 fluxes diagnosed from Wind-inter (black line), Wind-clim (green line) and ΔpCO2-clim (red line) during 1958-2016 for the entire tropical Pacific (18°S–18°N) (a), the Niño3 region (b) and the Niño4 region (c), respectively. The results are shown for smoothed values with 13-month running mean

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Due to the effect of anthropogenic activity, global atmospheric pCO2 has been continuously increasing from 1948 (315 ppm) to 2017 (406 ppm) (https://www.esrl.noaa.gov/gmd/ccgg/trends/full.html) (Fig. 9; blue line). Therefore, interdecadal change of ΔpCO2 is mainly attributed to variability of sea surface pCO2. Observational records of ocean surface pCO2 in the central equatorial Pacific show that sea surface pCO2 increased at a similar rate to the atmospheric CO2, which leads to zero trend in ΔpCO2 since 1980s (DiNezio et al. 2015). The modeled results are consistent with observational records, and ΔpCO2 appears to be zero-trend during the last two periods in the tropical Pacific (41.44 ppm during 1976–1997, 41.54 ppm 1998–2012) (Table 2, Fig. 9a). The near-zero change of ΔpCO2 is strikingly evident in the Niño3 region (119.22 ppm during 1976–1997, 118.78 ppm 1998–2012) (Fig. 9b and Table 2). In addition, the results from the fifth phase of the Coupled Model Intercomparison Project (CMIP5) and large member ensemble of simulations from CESM show a decrease trend in ΔpCO2 during the period of 2030–2070 when atmospheric CO2 increases (DiNezio et al. 2015). Therefore, the nearly zero trend of ΔpCO2 indicates that interdecadal variability of sea surface pCO2 may mask the anthropogenic forcing induced change on long-term trend of ΔpCO2 in the tropical Pacific.

Fig. 9
figure 9

Mean fields of sea surface pCO2, atmospheric pCO2 and ΔpCO2 during 1958–2016 for the entire tropical Pacific (18°S–18°N) (a), Niño3 region (b) and Niño4 region (c). The results are shown for smoothed values with 13-month running mean

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However, in the Niño4 region, interdecadal variability of ΔpCO2 is still obvious (74.51 ppm during 1976–1997, 79.28 ppm 1998–2012) (Table 2, Fig. 9c). Meanwhile, large interdecadal variability of wind speed is also located in the Niño4 region (Fig. 4b). Thus, the combined effects of both wind speed and ΔpCO2 act to strengthen interdecadal variability of CO2 fluxes in the western-central equatorial Pacific. In the Niño3 region, the changes of ΔpCO2 during the last two periods are very small. This relatively small change in ΔpCO2 partially can explain why the contribution of ΔpCO2 to CO2 fluxes is small in the eastern equatorial Pacific (Table 2).

3.5.1 A component analysis of sea surface pCO2

Figure 9 shows that interdecadal ΔpCO2 variability is mainly determined by variability of pCO2 at sea surface (Eq. 1), which is influenced by DIC, SST, SSS and alkalinity. To assess the relative contributions of different components, we conducted a component analysis developed by Takahashi et al. (1993) as follows (Eq. 3),

$$\frac{{dpCO_{2} }}{dt} = \frac{{\partial pCO_{2} }}{\partial DIC}\frac{dDIC}{dt} + \frac{{\partial pCO_{2} }}{\partial T}\frac{dT}{dt} + \frac{{\partial pCO_{2} }}{\partial ALK}\frac{dALK}{dt} + \frac{{\partial pCO_{2} }}{\partial S}\frac{dS}{dt}$$
(3)

where pCO2 is sea surface partial pressure of CO2; DIC is concentration of dissolved inorganic carbon within the mixed layer; T is sea surface temperature; ALK is total alkalinity and S is sea surface salinity. According to Table 8.3.1 in Sarmiento and Gruber (2006), we take

$$\frac{1}{{pCO_{2} }}\frac{{\partial pCO_{2} }}{\partial T} = 0.0423\;^{ \circ } {\text{C}}^{ - 1}$$
$$\frac{S}{{pCO_{2} }}\frac{{\partial pCO_{2} }}{\partial S} = 1$$
$$\frac{ALK}{{pCO_{2} }}\frac{{\partial pCO_{2} }}{\partial ALK} = - 8.9$$
$$\frac{DIC}{{pCO_{2} }}\frac{{\partial pCO_{2} }}{\partial DIC} = 9.5$$

Figure 10 shows that sea surface pCO2 exhibits pronounced interdecadal variability; i.e. sea surface pCO2 increases during the cold phase (1958–1975, 1998–2012), but decreases during the warm phase (1976–1997) of the IPO (Fig. 10). The contribution due to SST is out of phase with that due to DIC, indicating that the contributions from SST and DIC tend to cancel out each other on interdecadal timescale, whereas the contributions due to salinity and alkalinity effects to sea surface pCO2 are small. During the IPO positive phase, an increase in SST leads to an increase in seawater pCO2 due to thermodynamics (Fig. 3b, black dash line). In contrast, weak upwelling and vertical mixing during this warm phase of the IPO bring the subsurface water with lower DIC into the upper layer, acting to decrease the seawater pCO2. During the cold phase of the IPO (1958–1975, 1998–2012), an increase in trade winds leads to an enhanced upwelling and vertical mixing, which leads to a decrease in SST and an increase in DIC. Nevertheless, a decrease in SST acts to reduce solubility of CO2 in the seawater, which tends to decrease the sea surface pCO2. As shown in Fig. 10, the change of sea surface pCO2 is in phase with that of DIC but out of phase with that of SST, indicating that DIC plays a dominant role in determining interdecadal variability of sea surface pCO2. Additionally, the change of \(\frac{{dpCO_{2} }}{dt}\) is slightly larger in the Niño4 region than that in the Niño3 region, suggesting that interdecadal change of sea surface pCO2 is stronger in the central equatorial Pacific.

Fig. 10
figure 10

Component analyses of sea surface pCO2 in the Niño4 region (a) and the Niño3 region (b). All variables are calculated over the three different periods (1958–1975, 1976–1997, and 1998–2012)

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3.5.2 Mixed layer DIC budget analysis: physical vs. biological processes

Based on the dominant effect of DIC on the sea surface pCO2 on interdecadal timescale, we also analyzed the DIC budget within the mixed layer. Related analyses have been conducted by previous studies on interannual to decadal timescales (Wang et al. 2006, 2015). The DIC budget within the mixed layer can be written as

$$\frac{\partial C}{\partial t} = - u\frac{\partial C}{\partial x} - v\frac{\partial C}{\partial y} - w\frac{\partial C}{\partial z} + C_{mix} - NCP - \frac{{FCO_{2} }}{h}$$
(4)

where C represents DIC concentration in the mixed layer; u, v, w are the zonal, meridional and vertical velocity, respectively; Cmix is vertical mixing and entrainment terms (the sum of mixing and advection terms are called physical term); NCP represents the biological process (including uptake and regeneration); FCO2 is air–sea exchange of CO2, i.e. CO2 fluxes (\(h\) is the mixed layer depth).

Figure 11a shows large interannual and interdecadal variabilities of DIC in the central-eastern equatorial Pacific. Due to the close relationship between La Niña (El Niño) activities and cold (warm) phases of the IPO (Lin et al. 2018; An 2018), frequencies of El Niño and La Niña events occurring can directly influence the variations of DIC on interdecadal timescale. For example, during the cold phase of the IPO, thermocline depth is shallow, which favors the occurring of La Niña events. Meanwhile, during La Niña events, the equatorial upwelling is enhanced, which consequently leads to an increase in DIC concentration in the eastern equatorial Pacific.

Fig. 11
figure 11

The interannual anomalies along the equator for DIC (a) and NCP (b) within the mixed layer during the period 1958–2016. The long-term trends are removed. The units are mmol C m−3 in a and mmol C m−3 days−1 in b

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Figure 12a, b show that ocean dynamic processes (including advection and mixing) dominate the interdecadal variability of DIC. The ocean dynamic processes lead to an increase in DIC during the cold phase of the IPO (1958–1975, 1998–2012), and a decrease during the warm phase of the IPO (1976–1997), especially in the central Pacific. This result indicates that DIC experiences interdecadal fluctuations in the central equatorial Pacific. Additionally, in the central Pacific, the contributions of each components (physical process, biological uptake and gas exchange) to DIC are gradually increased in these three periods, and interdecadal signals of these components are still evident (Fig. 12a). Overall, interdecadal signals of DIC overwhelm the long-term trend in the western-central Pacific.

Fig. 12
figure 12

Budget analyses of DIC in the Niño4 region (a) and the Niño3 region (b). The contributions of physical processes, which are divided into zonal advevction (denoted as uDIC), meridional advection (denoted as vDIC), and mixing and vertical advection [denoted as (mix + w)DIC], are shown for the Niño4 region (c) and Niño3 region (d), respectively. All variables are calculated over three different periods (1958–1975, 1976–1997, and 1998–2012), respectively. The units are mol C m−3 year−1

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However, in the eastern Pacific, the contributions of each components to DIC interdecadal change are reduced during these three sub-periods (Fig. 12b). During the last two periods (1976–1997 and 1998–2012), contributions from physical dynamic term and biological uptake in DIC show nearly zero change (Fig. 12b). For example, the contributions of the physical processes keep on hold in the Niño3 region. This is because an increase in upwelling during cold phase of the IPO is compensated for by the decrease in upwelling during long-term trend period induced by the global warming (Collins et al. 2010). These processes in turn modulate relative contributions of each components to long-trend of DIC in the eastern equatorial Pacific.

The biological process and air–sea gas exchange play vital roles in balancing physical processes in the DIC budget; the biological process removes most of DIC due to biological uptake and regeneration (Fig. 12a, b). Meanwhile, Fig. 11b shows a strong interannual variability of NCP, with large variability being located in the central equatorial Pacific, which is similar to that of CO2 fluxes. Biological uptake is tightly associated with biological activity, and exhibits a decreased trend during the twentieth century (Boyce et al. 2010). In addition, phytoplankton biomass exhibits an increased trend in the tropical Pacific during the recent 20 years (Sharma et al. 2019). The combined effects of long-term trend and interdecadal change in biological uptake contribute to a zero-change of DIC during the last two periods in the eastern Pacific (Fig. 12b).

Due to the dominant roles played by physical processes in interdecadal variability of DIC, these terms (zonal, meridional advection, and the vertical mixing and advection terms of DIC) in the Niño3 and Niño4 region are shown separately in Fig. 12c, d. In the central equatorial Pacific (Fig. 12c), zonal DIC advection and vertical mixing of DIC tend to be compensated for meridional DIC advection, with their net differences being dominated by contributions of physical processes in Fig. 12a. Noteworthy, the meridional advection is stronger than vertical mixing and zonal advection, and exhibits clear interdecadal fluctuations in the Niño4 region.

In the eastern equatorial Pacific (Fig. 12d), vertical mixing dominates interdecadal variability of DIC and overwhelms the sum of zonal and meridional advection. Moreover, the interdecadal change in physical term of DIC budget exhibits a near-zero trend during the last two periods (1976–1997 and 1998–2012), which may be the reason why the change of ΔpCO2 is very small in the eastern equatorial Pacific. Overall, in responses to the regime shift of the IPO, the change in dynamical process affects the interdecadal variability of DIC, with its effects on DIC being most significant in the central equatorial Pacific. Consequently, the remarkable interdecadal change of DIC contributes to that of sea surface pCO2 in the central equatorial Pacific.

4 Discussion

CO2 fluxes are mainly determined by atmospheric wind speed and ΔpCO2 at the air–sea interface. On one hand, because the wind speed exhibits quadratic dependence on gas transfer velocity, it can influence the magnitude of CO2 fluxes. On the other hand, the sign of CO2 fluxes is determined by ΔpCO2. Therefore, ΔpCO2 is the factor that determines whether the ocean is a source or sinks for CO2, while wind speed can amplify or reduce the magnitude of releasing or absorbing CO2 at the sea surface. At present, how CO2 fluxes are affected by these two factors and their relative contributions on interdecadal timescale have not been understood well.

In this study, a modeling study and corresponding analysis are performed. Two apparent regime shifts of air–sea CO2 fluxes in the tropical Pacific are found in 1975–1976 and 1997–1998, which are associated with the regime shift of the IPO (Chen and Tung 2018). Since 2000s, a La Niña-like cooling associated with the cold phase of the IPO emerges in the eastern tropical Pacific; this period is often called global warming hiatus (Kosaka and Xie 2013). However, a possible ending of global warming hiatus occurred during 2014–2016 (Hu and Fedorov 2017). Meanwhile, a sharp decline of ΔpCO2 by 20 ppm is remarkable in Fig. 9 during 2014–2016. This is because sea surface pCO2 exhibits little change during 2012–2016, but atmospheric pCO2 (pCO2air) continuously rises due to anthropogenic activity. As discussed in Hu and Fedorov (2017), the possible ending of global warming hiatus may be linked to the phase change in the IPO from its cold phase to warm phase. During the warm phase of the IPO, weakened trade winds and upwelling can result in a decrease in DIC and ΔpCO2. In addition, under global warming scenario, weakened trade winds also lead to a weakening of the equatorial upwelling, causing reductions in DIC and ΔpCO2. Thus, a decrease in ΔpCO2 due to the warm phase of the IPO is superimposed onto a decline trend of seawater ΔpCO2 due to global warming, which may further reduce the ΔpCO2 in the next warm phase of the IPO. Consequently, the decrease in ΔpCO2 and wind speed due to global warming may lead to a reduction of CO2 fluxes in the next several decades. In the north Pacific subtropical gyre, Sutton et al. (2017) found that warm anomalies drove elevated seawater pCO2, and caused this region to be a net CO2 source for the first time in the observational records. They further suggested that climatic forcing could influence the timing of regional oceanic shift from a sink to a source. Whether the sign of ΔpCO2 can be changed from positive to negative in some region is important to the carbon cycle in the tropical Pacific, which should be investigated in the future.

Gu and Philander (1997) found that the link between the tropics and the extratropics (whose effects are rapid and poleward in the atmosphere but slow and equatorward in the oceans) can cause the interdecadal fluctuation in the Pacific. Zhang et al. (1998) presented observational evidence for decadal changes in ENSO that may originate from mid-latitude decadal variability. In this study, clear links between the tropics and the extratropics are found in the interdecadal anomalies of CO2 fluxes (Fig. 7). Recent studies show that the reemergence of anthropogenic CO2 through the recirculation within the subtropical cells can lead to the reduction of CO2 uptake in the surface ocean, which can potentially induce a positive climate-carbon feedback (Zhai et al. 2017). The interaction between the tropics and extratropics on interdecadal variability of CO2 fluxes should be investigated in the future.

In addition, the choice of wind speed products can exert significant influence on the calculation of CO2 fluxes. In this study, we only employ wind products from the NCEP/NCAR reanalysis to calculate the CO2 fluxes, but the uncertainty in wind fields can induce 30–37% change of CO2 fluxes in the mean global ocean carbon uptake (Roobaert et al. 2018). For projection on future interdecadal variability of CO2 fluxes, the accuracy of wind speed projection can significantly affect the global carbon cycle and even further climate change. Also, the results are obtained from a layer model; other level ocean models need to be used to perform similar experiments (e.g. Kang et al. 2017).

5 Summary

It is well recognized that the equatorial Pacific is the largest natural source region for CO2 fluxes, which accounts for 70% interannual variability of global CO2 fluxes. However, the interdecadal variability of CO2 fluxes in this region has not been understood well. Here, we examine the interdecadal variability of CO2 fluxes by using a coupled ocean physics–biogeochemical model forced by prescribed wind from NCEP/NCAR reanalysis during 1948–2016. Two regime shifts are found in 1975–1976 and 1997–1998, which are consistent with the phase transitions of the interdecadal Pacific Oscillation (IPO). Modelling results indicate that the ΔpCO2 has a near-zero trend in the recent two phases (1976–1997 and 1998–2012), which are related to the global warming hiatus. However, the rebound of CO2 fluxes in recent decades (1998–2012) is mainly determined by the increase in wind speed. Additionally, one major finding from this study is that the large interdecadal variability region of CO2 fluxes is concentrated on in the central equatorial Pacific. The relationships between CO2 fluxes and wind speed variability indicate that their interdecadal fluctuations are mostly pronounced in the central-western tropical Pacific, but not in the eastern Pacific. Overall, the interdecadal variability of wind speed plays a key role in determining that of CO2 fluxes. The contribution from the ΔpCO2 to interdecadal variability of CO2 fluxes is relatively small.

The interdecadal variability of CO2 fluxes can partly mask the decreased trend in outgassing CO2 in the equatorial Pacific and further increase the uncertainty in projection on ocean sink for anthropogenic CO2, which in turn has a significant influence on the atmospheric CO2 level. Due to the importance of the equatorial Pacific in the global carbon cycle, interdecadal fluctuations of CO2 fluxes may exert a significant influence on the carbon sink of global ocean under the scenario of global warming. These relationships need to be investigated in the near future.