Trends in pCO₂ and sea–air CO₂ flux over the global open oceans for the last two decades

Abstract

To date, millions of data for partial pressure of carbon dioxide in surface seawater (pCO₂s) have been acquired from global oceans. However, pCO₂s varies extremely both in space and time, and it is still necessary to fill in its spatiotemporal gaps to evaluate the changes in sea–air CO₂ flux from regional to global scales. In the present study, we have analyzed the rates of pCO₂s increase for the past decades, ranging from +1.21 µatm year⁻¹ in the western equatorial Pacific to +2.00 µatm year⁻¹ in the Southern Ocean, and developed algorithms to reconstruct global monthly pCO₂s fields based on a quality-controlled database, Surface Ocean CO₂ Atlas (SOCAT) version 2. The error of pCO₂s algorithms is ±16.3 µatm. The mean annual global sea–air CO₂ flux for the years 1990–2012 was estimated to be −1.76 PgC year⁻¹ (contemporary flux; a negative value indicates oceanic uptake). The uncertainty in this estimate is calculated to be 0.77 PgC year⁻¹ (44 %), i.e., 0.09 PgC year⁻¹ from our empirical method to interpolate/extrapolate pCO₂s, and 0.67 PgC year⁻¹ from determination of the rates of pCO₂s increase and the rest from gas transfer processes including wind speed (0.26 PgC year⁻¹) and a scaling factor of piston velocity (0.26 PgC year⁻¹). The decadal mean CO₂ flux showed a trend toward increasing uptake from −1.67 PgC year⁻¹ for 1990–1999 to −1.92 PgC year⁻¹ for 2003–2012, due to growing uptake in the Pacific and Atlantic Oceans. However, these estimates of CO₂ flux are sensitive to the rates of pCO₂s increase used to constrain the long-term pCO₂s change for each sub-region.

Appendix: Derivation of equations to estimate surface ocean CO2 mol fraction

In this appendix, we describe derivation of equations to estimate surface ocean CO₂ mole fraction (xCO₂s) calculated from the data of measurement collected in Surface Ocean CO₂ Atlas version 2 (SOCAT V2; Bakker et al. 2014) and satellite chlorophyll-a data by multiple linear/nonlinear regressions.

$$x{\text{CO}}_{2} {\text{s}} = f\left( {{\text{SST}}, {\text{SSS}}, {\text{Chl-}}a} \right)$$

(5)

Sampling frequencies of xCO₂s in SOCAT vary largely in space and time. To reduce the impacts of the sampling bias on analysis, sub-hour data were binned to hourly ones. As xCO₂s and SST are thought to have trends toward increase in recent decades, we normalized data of xCO₂s and SST to those at the reference year A.D. 2000. Analyses of the rate of xCO₂s increase for each region were made as described in Sect. 2.2.1. Trends toward SST increase were also analyzed for “Merged satellite and in situ data Global Daily Sea Surface Temperatures” (MGDSST) in the same manner. It is appropriate to use normalized xCO₂s as a dependent variable and normalized SST, SSS and Chl-a as independent ones in multiple regression for the calculation of xCO₂s in the reference year, and to adjust it to xCO₂s through the period using mean rates of xCO₂s increase. In the case that significant increases in SSS and/or Chl-a exist, the change in xCO₂s resulted from these effects are double-counted for calculated xCO₂s values. However, these trends were not taken into account because the rates of SSS and Chl-a changes were very small (<0.01/year). The details of derivation of equations for the Pacific, Atlantic, Indian and Southern Ocean are explained below. The data sets used are listed in Table 1. Chl-a used for the regressions were 0.25° × 0.25° monthly binned data; that is, we used the Chl-a data in grids where xCO₂ observations were performed at the same month.

1.1 Pacific Ocean

We divided the Pacific Ocean into 14 regions (Fig. 6), following Sugimoto et al. (2012). The borders of these regions are geographically variable with time, since they have been defined on the basis of SST and/or SSS. This is particularly the case for the equatorial zone. The equatorial zone is divided into three sub-regions, i.e., western warm pool (PEQ-1), equatorial divergence zone (PEQ-2), and eastern low salinity region (PEQ-3). Once a warm event of El Niño Southern Oscillation occurs, equatorial divergence zone retreats and the western warm pool expands to the east.

Fig. 6

Schematic map of regions in the pCO₂s estimate for the Global Ocean. Curved lines indicate borders defined with SST or SSS and straight lines indicate borders defined with latitude and longitude. NPA Subarctic North Pacific, NPA-1 Northern subarctic, NPA-2/3 Central subarctic, NPA-4 Southern subarctic, NPT Subtropical North Pacific, NPT-1 Western subtropics, NPT-2 Northeastern subtropics, NPT-3 Southeastern subtropics, NPT-4 Off of Costa Rica, PEQ Equatorial Pacific, PEQ-1 Western warm pool, PEQ-2 Equatorial upwelling, PEQ-3 Eastern low salinity, SPT Subtropical South Pacific, SPT-1 Subtropics, SPT-2 Off of Peru, SPA Subantarctic South Pacific, SPA-1 Northern subantarctic, SPA-2 Southern subantarctic, NAA Subarctic and Arctic North Atlantic, NAA-1 Arctic, NAA-2 Labrador Sea, NAA-3 Northwestern subarctic, NAA-4 Northeastern subarctic, NAA-5 Central western subarctic, NAA-6 Central eastern subarctic, NAA-7 Southern subarctic. NAT Subtropical North Atlantic, NAT-1 Subtropics, NAT-2 Off of Guinea, AEQ Equatorial Atlantic, AEQ-1 low salinity region, AEQ-2/3/4 high salinity region, SA South Atlantic, SA-1 Northern subtropics, SA-2 Off of Angola, SA-3 Western subtropics, SA-4 Central subtropics, SA-5 Eastern subtropics, SA-6 Subantarctic, ARB Arabian Sea (seasonally divided into one to three subregions), BGL Bay of Bengal, IEQ Equatorial Indian Ocean, IEQ-1/2 Western equatorial, IEQ-3 Eastern equatorial, SI Southern Indian Ocean, SI-1/2 Northern subtropics, SI-3/4 Southern subtropics, SI-5/6 Subantarctic, SO-1 Southern Ocean high SST, SO-2 Southern Ocean medium SST, SO-3 Southern Ocean low SST

The equations of xCO₂s for 14 regions in the Pacific are summarized in Table 3. Details of these equations have been described in Sugimoto et al. (2012), but were partly modified in this work, because we used the database of sea surface CO₂ of SOCAT V2 while Sugimoto et al. (2012) used that of LDEO V1.0 (Takahashi et al. 2008) to derive the equations. These empirical equations to estimate xCO₂s were obtained by multiple regressions with SST and SSS. In addition, Chl-a was used to account for biological CO₂ uptake in the northern and central subarctic zones (NPA-1 to NPA-3). For central subarctic zone, different equations are applied to summer and winter. In the subtropical western North Pacific, the dependencies of xCO₂s on SST were determined in every 1° zonal band every year based on the operational time-series observations along 137°E and 165°E conducted by Japan Meteorological Agency. The relationship was used to estimate xCO₂s in the region NPT-1, as described in Murata et al. (1996). In the subtropical South Pacific (SPT-1), we assumed that the same functional form between SST and xCO₂s as in the subtropical North Pacific NPT-1 can be applied, and determined the relationship between SST and xCO₂s. Here, a climatological apparent dependence of xCO₂s on SST was obtained for each 1° in latitude from the data normalized at A.D. 2000. An offset was calculated in every 1° × 1° from the climatological dependence and observations in the grid.

1.2 Atlantic Ocean

We used similar methods to those of the Pacific Ocean to empirically estimate xCO₂s in the Atlantic Ocean. The empirical equation of xCO₂s in each of 19 regions of the Atlantic is described in Table 4. The distinct features in the Atlantic are the large contrasts in SST and SSS between the eastern and the western regions and the high primary production in the northern North Atlantic (NAA-1–7), as well as a moderate upwelling and large river-discharges into the equatorial zone (AEQ-1–4). More details of the equations are described below.

1.2.1 Subarctic and arctic North Atlantic (north of 35°N, NAA-1–7)

The relationship between SST and xCO₂s (normalized to the values in A.D. 2000, the same applies hereafter) in the subarctic zone of the North Atlantic is shown in Fig. 7a. In this zone, xCO₂s is positively correlated with SST when SST is higher than 17 °C (NAA-7). In this warmer domain, nutrients are depleted in surface water and biological activities are moderate, and therefore the region has a nature similar to that of the subtropics. The region south of 40°N and west of 30°W, i.e., the path of the Gulf Stream, also has the nature of the subtropics to be mentioned in "Subtropical North Atlantic (12°N–35°N, NAA-8, 9)", and the same method was applied for this region.

Fig. 7

Relationships between xCO₂s and SST in the Atlantic Ocean (a Subarctic North Atlantic, b Subtropical North Atlantic, c Equatorial Atlantic and d South Atlantic), the Indian Ocean, [e–h Arabian Sea (e NE monsoon, f pre-monsoon, g SW monsoon and h post-monsoon), i Bay of Bengal, j equatorial Indian and k southern Indian Ocean], and l Southern Ocean. Black/grey plots on a are for winter/summer, black/grey plots on b are for off Guinea/other subtropics, black/grey plots on c are for non-upwelling/upwelling season, black/grey plots on d are for north/south of 20°S, black/grey plots on e are for southwestern/northeastern region, black/grey plots on g are for northwestern/southeastern region, black/grey plots on h are for west/east of 64°E, black/darkgrey plots on j are for west of 60°E in southwestern monsoon/other seasons and lightgrey plots are for east of 60°E, black/grey plots on k are for north/south of 25°S, and black/grey plots on l are for winter/summer

In winter (December–March), xCO₂s correlates positively/negatively with SST in the SST range lower/higher than around 6–8 °C (Fig. 7a). The higher SST domain corresponds to the eastern region where North Atlantic Current prevails and the lower SST domain corresponds to the western region where the subarctic gyre prevails. Nakaoka et al. (2006) also reported positive SST–xCO₂s correlations in the Barents Sea and the Greenland Sea where SST is lower (SST < 8 °C). We defined the threshold where correlations changes as SST = 7.6 °C in the northern subarctic (55–65°N: NAA-3, or NAA-4) and 7.0 °C in the central subarctic (south of 55°N: NAA-5 or NAA-6). The Arctic (NAA-1) was separated into the regions to the north of 65°N and Labrador Sea (NAA-2), and was distinguished from other regions by its lower SST and SSS (SST < 7.0 °C and SSS < 34.8 in the area west of 45°W and north of 52°N).

From spring through autumn (April–November), xCO₂s in these regions drops down due to the large biological CO₂ uptake, and therefore xCO₂s negatively correlates with Chl-a, as discussed by Olsen et al. (2008) (Fig. 8a). In order to estimate the contribution of biological activity to the xCO₂s drawdown, we calculated the differences between xCO₂s values estimated by the empirical equations for winter and those from measurements in summer, and regarded the difference as the contribution from biological activity in summer. These differences, named the term “Bio”, were then fitted with logarithms of Chl-a. A negative value for Bio indicates that xCO₂s calculated from SST and SSS needs correction for the biological CO₂ uptake. The value of Bio was added to the empirical equation in the months when it had a negative value from April through November.

Fig. 8

Relationships between xCO₂s and Chl-a in a Subarctic North Atlantic, b Southern Indian Ocean and c Southern Ocean

1.2.2 Subtropical North Atlantic (12°N–35°N, NAA-8, 9)

The relationship between SST and xCO₂s in the subtropical zone of the North Atlantic is shown in Fig. 7b. In general, xCO₂s is positively correlated with SST, but varies largely (~100 μatm) at the same SST. This relationship is similar to that in the subtropical North Pacific and is likely to be ascribed to the spatial variation in the apparent dependence of xCO₂s on SST. Two examples of the SST–pCO₂s relationship at time-series stations, Bermuda Atlantic Time-Series (BATS) and European Station for Time-series in the Ocean (ESTOC), are shown in Fig. 9. The plotted data are based on Bates et al. (2012) and González-Dávila and Santana-Casiano (2009). pCO₂s at BATS were calculated from total inorganic carbon and total alkalinity. These stations are located at a similar latitude (BATS: 30°40′N, ESTOC: 29°30′N), whereas BATS lies in the western and ESTOC lies in the eastern subtropical North Atlantic. Slope of the apparent dependencies of pCO₂s on SST are similar to each other, but pCO₂s in ESTOC is ca. 30 μatm higher than in BATS at the same SST. It is likely that the slope changes with latitude and the intercepts change with longitude, as is case in the North Pacific subtropics. We used the data taken to the west of 60°W, where they distribute rather evenly, to calculate a slope for each 1° latitude. An intercept (xCO₂s at SST = 25 °C) for each 1° × 1° pixel was calculated using this slope and data in the pixel in the region.

Fig. 9

Relationships between pCO₂s and SST at two time-series stations, BATS (black circle) and ESTOC (grey square). BATS and ESTOC during the period from 2005 to 2009. pCO₂s in BATS are calculated from dissolved inorganic carbon and total alkalinity. The data for BATS are based on Bates et al. (2012) and for ESTOC on González-Dávila and Santana-Casiano (2009)

A strongly negative SST–xCO₂s correlation is seen at SST < 22 °C in the coastal upwelling area off of Guinea in western Africa. The relationship is similar to those reported in Oudot et al. (1987) and Lefèvre et al. (1998).

1.2.3 Equatorial Atlantic (8°S–12°N, AEQ-1–3)

The relationships of SST–xCO₂s and SSS–xCO₂s in the equatorial Atlantic are shown in Figs. 7c and 10a. It is clear from Fig. 10a that xCO₂s is positively correlated with SSS at low SSS region (SSS < 34.3). The low SSS extends around off the coast of northeastern South America, western Africa and along the intertropical convergence zone, and is ascribed to the large river discharges from the Amazon and Congo Rivers and the heavy rainfall. As reported by Lefèvre et al. (2010), these regions act as a sink for CO₂ because of low xCO₂s.

Fig. 10

Relationships between xCO₂s and SSS in a equatorial Atlantic and b Bay of Bengal. Black plots on a are for low-SSS region and dark/light grey plots for upwelling/non-upwelling seasons

In the higher SSS region (SSS ≥ 34.3), the SST–xCO₂s relationship is seasonally variable. For the months from May through December when the equatorial upwelling is stronger, xCO₂s is negatively correlated with SST. This negative relationship is similar to that found from the data of moored buoy PIRATA at 6°S–10°W (Parard et al. 2010). For other months (January–April), xCO₂s is positively correlated with SST (Fig. 7c) and western and eastern regions have different correlations. A positive correlation is seen between SSS and xCO₂s as well (Fig. 10a).

1.2.4 South Atlantic (south of 8°S, SA-1–6)

The relationship between SST and xCO₂s in the South Atlantic is shown in Fig. 7d. In the region to the north of 20°S (SA-1 and 2), a positive/negative correlation between SST and xCO₂s was found in the region where SST is higher/lower than 22 °C. The positive correlation here is similar to those found in the subtropics of other basins. The negative correlation is thought to have been caused by the coastal upwelling off of Angola (SA-2), as reported by Santana-Casiano et al. (2009).

In the south of 20°S, xCO₂s is positively correlated with SST when SST is higher than 15.5 °C. A similar correlation is also seen in subtropics of the other basins. We divided this region into three subregions (SA-3, 4 and 5), since the dependence of xCO₂s on SST in the western boundary is thought to differ from that in other subtropical regions and the eastern region has been affected by the Indian Ocean. In the subantarctic region where SST is lower than 15.5 °C (SA-6), xCO₂s shows negative correlations with SST and with Chl-a, as in the North Pacific and subpolar regions in other basins. The region where SST is lower than 11 °C will be discussed in the "Southern Ocean".

1.3 Indian Ocean

The zonal distribution of xCO₂s in the southern Indian Ocean is similar to those in the South Pacific and in the South Atlantic, and therefore we use similar schemes in estimating xCO₂s. The northern Indian Ocean has a more complex structure of xCO₂s variability because of the influences of the Indian monsoon and large rivers of South Asia. The sub-regions defined in estimating xCO₂s in the Indian Ocean are shown in Fig. 6 and the empirical equation of xCO₂s for each sub-region is described in Table 5.

1.3.1 Arabian Sea and Bay of Bengal (north of 5°N, ARB-1–8, BGL)

The Indian monsoon is a dominant factor controlling the variability of xCO₂s in the Arabian Sea (Sabine et al. 2000; Sarma 2003; Bates et al. 2006). The SST–xCO₂s relationships in winter northeast monsoon, in spring pre-monsoon, in summer southwest monsoon and in autumn post-SW monsoon seasons are shown in Fig. 7e–h, respectively. In this work, we define the seasons as (1) NE monsoon [December–March (SST < 26 °C for December and March)], (2) pre-monsoon [March–May (SST ≥ 26 °C for March)], (3) SW-monsoon (June–September) and (4) post-monsoon (October–December (SST ≥ 26 °C for December). We used an additional data set from U. S. Joint Global Ocean Flux Study in 1995 (Millero et al. 1998; Goyet et al. 1998) because the number of data in Arabian Sea is insufficient to derive algorithms.

In the NE monsoon season, xCO₂s is negatively correlated with SST in the northeastern region (north of 21°N and east of 64°E) when SST is lower than 26 °C, because winter convective mixing cools the seawater and brings CO₂ to surface. In the rest of the region, xCO₂s is positively correlated due primarily to the thermodynamic effect of SST on xCO₂s (Fig. 7e). In the pre-monsoon season, xCO₂s is also positively correlated with SST over the Arabian Sea (Fig. 7f).

In the SW monsoon season, the coastal upwelling caused by the monsoon heavily effects on the distributions of SST and xCO₂s in the Arabian Sea. SST decreases to 20–23 °C and xCO₂s increases to 600–740 ppm, especially in northwestern region. However, there is also a region where the effect of SW monsoon is insignificant (SST >28 °C) and the level of xCO₂s is moderate (~400 ppm) (Fig. 7g). Accordingly, we define three sub-regions in this season; the northwestern region where highly affected by the monsoon, the southeastern region where the effect is moderate, and the high SST region where it is insignificant.

In the post-monsoon season, the upwelling ceases and has no effect on the variability of xCO₂s. Since the apparent dependence of xCO₂s on SST is different between eastern and western regions (Fig. 7h), we divided this region into these two sub-regions partitioned at 64°E and derived the equation for each of the sub-regions.

In the Bay of Bengal, xCO₂s is positively correlated with SST and SSS (Figs. 7i, 10b) as found by Kumar et al. (1996). The low salinity in the Bay of Bengal is attributed to the discharges from the Ganga-Bramaptra and Ayeyarwady Rivers. As this effect does not vary seasonally, we apply one equation to all seasons to estimate xCO₂s.

1.3.2 Equatorial Indian Ocean (10°S–5°N, IEQ-1–3)

We divided the equatorial zone of the Indian Ocean into two sub-regions by the longitude at 60°E. The relationships of SST–xCO₂s in the equatorial Indian Ocean are shown in Fig. 7j. The effect of equatorial upwelling on xCO₂s has not been found in the Indian Ocean, but seasonal drop-down of SST due to the coastal upwelling has been seen in the region off of Somalia to the west of 60°E in the southwest monsoon season. This makes the slope of SST–xCO₂s relationship smaller than the one due to thermodynamic effect. By contrast, the SST–xCO₂s relationship is dominated by the thermodynamic effect in the region to the east of 60°E.

1.3.3 Southern Indian Ocean (south of 10°S, SI-1–6)

The relationship between SST and xCO₂s in the southern Indian Ocean is shown in Fig. 7k. Like in the Pacific and in the Atlantic, xCO₂s is positively correlated with SST in the subtropics where nutrients are depleted, and is negatively correlated in the subpolar region where nutrients are abundant. The boundary between these regions locates near the subtropical front and is oscillating seasonally in the SST range between 15 and 20 °C (Poisson et al. 1993). On the basis of these observations, we divided the southern Indian Ocean into six domains, i.e., winter (May–November) and summer (December–April) in each of three zones, including the northern subtropics (SI-1/2), the southern subtropics (SI-3/4), and the subantarctic (SI-5/6). Northern and southern subtropics are partitioned at 25°S. Southern subtropics and subantarctic are partitioned with an isotherm of 16 °C in summer and 18 °C in winter. In the subantarctic in summer, a negative correlation between Chl-a and xCO₂s (Fig. 8b) was also found, and was used to derive empirical equations.

1.4 Southern Ocean

The Southern Ocean is considered to be playing a large role for carbon uptake from the atmosphere and storage in the ocean interior through the formations of the Subantarctic Mode Water and the Antarctic Intermediate Water, followed by their mass transportation to the lower latitudinal zones (e.g., Iudicone et al. 2011; Sallée et al. 2012; Khatiwala et al. 2013). However, a large seasonal variation of xCO₂s has been observed in the Southern Ocean. It is a net source of CO₂ to the atmosphere in winter when vertical mixing is enhanced, and is a net sink in summer when primary production is activated (e.g., Metzl et al. 1999; Ishii et al. 2002; Chierici et al. 2012). The large temporal and spatial variability of xCO₂ and paucity of measurements, as well as the complex meridional overturning circulation, is making it difficult to estimate xCO₂s from measurements as well as from modelling (Takahashi et al. 2009; Lenton et al. 2013).

The relationship between SST and xCO₂s in the Southern Ocean is shown in Fig. 7l. Here, we defined the Southern Ocean as the region where SST is lower than 11 °C. In winter, variability of pCO₂s is smaller and the relationship between SST and xCO₂s changes at SST of around 8 and 3 °C. We divided the regions into three sub-regions by these SST to make empirical equations (Fig. 6). We did not use the data in the coldest regions of ice margin where SST is lower than 0.7 °C. In this region, xCO₂s varies greatly even in winter, possibly because of the variability in the effect of the entrainment of the CO₂-rich subsurface water.

In summer, the drawdown of xCO₂s as a result of the biological xCO₂s uptake is evident. The relationship between Chl-a and xCO₂s in the Southern Ocean in summer is shown in Fig. 8c. Estimated xCO₂s is corrected for the biological CO₂ uptake in summer with the same methods as those for the Arctic and subarctic North Atlantic, described in S2.1. The empirical equation of xCO₂s for each sub-region is described in Table 6.

1.5 Calculation of pCO₂s

Based on the empirical equations described in the previous sections, monthly 1° × 1° pCO₂s fields were obtained globally, except for the Arctic Ocean, marginal seas and coastal zones (see Fig. 3), for the period from 1990 through 2012 using the data sets listed in Table 1. Monthly climatologies of Chl-a were used for pCO₂s calculation before 1998. In the restricted areas/months, including the North Pacific north of 49°N/December, the North Atlantic north of 68°N/October and of 56°N/November, no Chl-a data were available and we assumed Chl-a as zero. This assumption is not problematic, because biological production is expected to have a minimal effect on pCO₂s in these areas/months.

1.6 The uncertainty in pCO₂s estimate

Root mean square errors (RMSE) and biases were calculated from Eqs. (6) and (7),

$${\text{RMSE}} = \left( {\mathop \sum \nolimits \left( {p{\text{CO}}_{{2{\text{est}}}} - p{\text{CO}}_{{2{\text{obs}}}} } \right)^{2} /N} \right)^{0.5}$$

(6)

$${\text{Bias}} = \mathop \sum \nolimits \left( {p{\text{CO}}_{{2{\text{est}}}} - p{\text{CO}}_{{2{\text{obs}}}} } \right)/N$$

(7)

where pCO_2est and pCO_2obs denote the estimated and the measured pCO₂s value, respectively, and N indicates a number of the pair of data. Here, pCO_2obs are the monthly 1° × 1° binned data of measurements.

The meridional distributions of mean RMSEs and biases for each 5° zonal band are shown in Fig. 11. Biases are attributable to the differences between the binned in situ SST/SSS data ancillary to fCO₂s measurements and those in data sets listed in Table 1. Biases are mostly within ±10 μatm, and are smaller (2–3 μatm) in the mid-latitudes of the northern hemisphere. RMSE in the mid-latitudes and in the equatorial Pacific ranges between 10 and 20 μatm and between 20 and 25 μatm, respectively. RMSE in the high latitudes is even higher (20–50 μatm) because of the enhancement of biological CO₂ uptake in summer, but has been reduced by using Chl-a, except for in the regions to the north/south of 65°N/S where sea ice influences both hydrography and biogeochemistry. In subpolar and polar zones, large but short spatial and temporal variations in Chl-a, as often seen in the in situ measurements, have not been resolved in the 1° × 1° monthly Chl-a data set. To the north of 10°N in the Indian Ocean, where high pCO₂s associated with the southwest monsoon are observed, biases negatively exceed −7 μatm and RMSEs are larger (22–59 μatm) than those in other regions. It is likely that measurements can capture large but short-time scale changes in pCO₂s, and that the rise in pCO₂s resulted from intense upwelling in SW-monsoon season in particular, but a monthly mean used to estimate pCO₂s does not. In the equatorial Pacific, absolute values of biases and RMSEs are both higher (e.g., bias is 10 μatm and RMSE is 24 μatm at the 10°–5°S zonal band), due to larger error in the marginal zone of the region for estimating pCO₂s. Overall, the global averaged bias of −0.9 μatm and RMSE of 16.3 μatm were estimated from area-weighted means. These bias and RMSE were derived from comparison between estimated values and the data used for regressions, but almost the same values of −1.9 and 18.1 μatm for global ocean were derived from comparison between them and independent pCO₂s data included in the LDEO V2013 database (Takahashi et al. 2014b), but not in SOCAT V2. The global RMSE of 16.3 μatm is almost the same as values from other studies such as Nakaoka et al. (2013), Sasse et al. (2013) and Zeng et al. (2014), and slightly higher than the value from Landschützer et al. (2014).

Fig. 11

Meridional distributions of 5° zonal mean RMSE (upper) and bias (lower) between estimated and observed pCO₂s. Biases are calculated by subtracting the observed value from the estimated one; therefore, a positive value indicates overestimation. Cross-shaped plots are for the Pacific Ocean (including Pacific sector of the Southern Ocean, the same hereinafter), filled circles are for the Atlantic Ocean, and open squares are for the Indian Ocean