Open Access Model Development

Air-sea CO2 fluxes over the Pacific Ocean are known to be characterized by coherent large-scale struc- tures that reflect not only ocean subduction and upwelling patterns, but also the combined effects of wind-driven gas exchange and biology. On the largest scales, a large net CO2 influx into the extratropics is associated with a robust seasonal cycle, and a large net CO2 efflux from the trop- ics is associated with substantial interannual variability. In this work, we have synthesized estimates of the net air-sea CO2 flux from a variety of products, drawing upon a vari- ety of approaches in three sub-basins of the Pacific Ocean, i.e., the North Pacific extratropics (18-66 N), the tropi- cal Pacific (18 S-18 N), and the South Pacific extratropics (44.5-18 S). These approaches include those based on the measurements of CO2 partial pressure in surface seawater (pCO2sw), inversions of ocean-interior CO2 data, forward ocean biogeochemistry models embedded in the ocean gen- eral circulation models (OBGCMs), a model with assimila- tion of pCO2sw data, and inversions of atmospheric CO2 measurements. Long-term means, interannual variations and mean seasonal variations of the regionally integrated fluxes were compared in each of the sub-basins over the last two decades, spanning the period from 1990 through 2009. A simple average of the long-term mean fluxes obtained with surface water pCO2 diagnostics and those obtained with ocean-interior CO2 inversions are 0.47± 0.13 Pg C yr 1 in


Introduction
The Pacific Ocean plays an important role in the climate system as a large sink for anthropogenic carbon dioxide (CO 2 ), and, thereby partially mitigates the large-scale effects of human CO 2 emissions into the atmosphere. Estimates of the net air-sea 15 CO 2 flux based on measurements of partial pressure of CO 2 in near-surface seawater (pCO 2 sw) and in the marine boundary air show that the extra-tropics in the North and South Pacific are major oceanic sinks of atmospheric CO 2 . Although the CO 2 uptake in these sub-basins is counteracted in part by the large CO 2 outgassing from the tropical zone, the integrated CO 2 uptake by the Pacific Ocean likely accounts for approximately 20 one third of the global oceanic CO 2 uptake (Takahashi et al., 2009a;Wanninkhof et al., 2013). In addition, it is well recognized that CO 2 outgassing from the tropical Pacific exhibits large variations with the El Niño Southern Oscillation (ENSO). This large interannual variability in air-sea CO 2 fluxes within the tropical Pacific is thought to play a dominant role in the inter-annual variability in the global oceanic CO 2 uptake (e.g., tional results with simulations from ocean models and estimates based on a combination of carbon data and models for the purpose of assessing fluxes over large temporal and spatial scales. Even then, there has been relatively poor agreement between the various approaches for estimating net air-sea CO 2 fluxes in the Pacific Ocean (McKinley et al., 2004;Peylin et al., 2005). 10 In this work, we begin with a review of what is known about air-sea CO 2 fluxes over the sub-basins of the Pacific Ocean. We then present a synthesis of state-of-the-art assessments of net air-sea CO 2 flux over the past two decades spanning the years from 1990 through 2009. This effort brings together CO 2 flux estimates from a wide range of available approaches: a synthesized climatological pCO 2 sw data set, diagnostic mod-15 els that use empirical interpolation schemes applied to the data of pCO 2 sw, oceanic inversion methods from measurements of ocean interior dissolved inorganic carbon (DIC) and ocean circulation models, prognostic ocean general ocean circulation models coupled with biogeochemical models (OBGCMs), a data-assimilation model with pCO 2 sw, and atmospheric CO 2 inversion systems with measurements of atmospheric Introduction to identify the factors that cause the differences in the estimate of the flux among the methods, so that the results presented here can serve to guide future research.

Tropical Pacific
The physical and biogeochemical properties in the surface layer of the tropical Pacific 5 show a large contrast between the domains of the western "warm pool" and the eastern "cold tongue" (Figs. 1 and 2). The warm pool is characterized by high sea surface temperatures (SST > 29.5 • C) and low sea surface salinities (SSS < 34.8) due to the large solar heat influx and high annual precipitation. As a result of the stratification thus attained, nitrate is depleted and the concentration of DIC is low (< 1950 µmol kg −1 10 when salinity-normalized at S = 35) in the surface layer of this region. Due to the near equilibration of surface water pCO 2 with atmospheric CO 2 , and the presence of low wind speeds, net air-sea CO 2 fluxes over the "warm pool" are relatively small (< 1 mmol m −2 day −1 ; e.g., Ishii and Inoue, 1995). By contrast, surface water in the eastern tropical Pacific cold tongue region tends to 15 be highly supersaturated with respect to atmospheric CO 2 . This is associated with the wind-driven equatorial divergence and turbulent mixing that brings colder, saline and nutrient-and CO 2 -rich subsurface waters to the surface. The cold tongue is characterized by lower SSTs (22 < T ( • C) < 29), higher SSSs (> 35), and higher DIC concentrations (> 1980 µmol kg −1 at S = 35) than in the western Pacific warm pool (e.g., Ishii 20 et al., 2004;see also Figs. 1 and 2). A significant portion of the DIC in the upwelled water is either removed by biological uptake or released to the atmosphere during the course of the poleward and westward advection. Nevertheless, pCO 2 sw remains higher than the atmosphere (pCO 2 sw−pCO 2 air > 90 µatm) due to the effect of concurrent warming (e.g., Feely et al., 1999Feely et al., , 2002Feely et al., , 2006Ishii et al., 2004; The "cold tongue" in the eastern tropics extends to the west during the cold events of ENSO (La Niña) and retreats to the east during the warm events of ENSO (El Niño). ENSO drives changes in the distributions of DIC, SST, and salinity in surface water as well as the surface wind field, and causes large perturbations to pCO 2 sw and significant temporal variability in the CO 2 outgassing from the tropical Pacific (e.g., Feely 5 et al., 1987, 2002Inoue and Sugimura, 1992;Ishii et al., 2004). The ENSOdriven changes to the variables that control pCO 2 sw and the gas transfer coefficient have been simulated and analyzed in a modeling study of Doney et al. (2009a, b). Their analysis revealed that the largest variability in air-sea CO 2 flux in the equatorial Pacific occurs in the region spanning the Date Line to the coast of Peru (Fig. 3). The dominant driver of this variability is the variability in DIC (Fig. 4). Although it is partly offset by the counteracting effect of variability in SST, the effect of DIC-driven changes in pCO 2 sw is reinforced by the effect of wind-speed change and results in the large variability in the air-sea CO 2 flux (see Figs. 3 and 4). A number of studies with OBGCMs have examined biogeochemical processes and air-sea CO 2 fluxes over the tropical Pacific 15 (e.g., Winguth et al., 1994;Le Quéré et al., 2000;Obata and Kitamura, 2003;McKinley et al., 2004McKinley et al., , 2006Wang et al., 2006;Christian et al., 2008;Doney et al., 2009a). These studies have shown the dominant role of the tropical Pacific in the global inter-annual variability in the oceanic CO 2 uptake.
Underlying the large interannual variability is a secular trend with increasing pCO 2 sw 20 observed in this region over the past decades (Feely et al., 1999(Feely et al., , 2006Takahashi et al., 2003). The mean rate of pCO 2 sw increase is consistent with the rate of atmospheric CO 2 increase, but decadal modulations have also been reported (Takahashi et al., 2003;Feely et al., 2006;Ishii et al., 2009). The decadal variability of pCO 2 sw is possibly linked with changes in the shallow meridional overturning circu-Introduction

North Pacific extra-tropics
In the extra-tropics, the dominant timescale of variability is the seasonal cycle. The predominance of this signal is expressed not only in SST, but also in large seasonal variations of mixed layer depth. Such seasonal variations in physical state variables are then associated with important seasonal variability in ocean biogeochemistry and 5 biological activity. The factors drive changes in DIC and pCO 2 sw. In the North Pacific, the seasonality of pCO 2 sw is particularly significant in the vicinity of the Kuroshio Extension Current and in the western subarctic zone including the western subarctic gyre and the Bering Sea (Takahashi et al., 2002) (Figs. 1 and 2). Throughout the majority of the North Pacific extra-tropics, particularly in the northern subtropical zone, cooling 10 in winter is the dominant control on low pCO 2 sw although it is partly compensated for by increases in DIC associated with wintertime vertical mixing (e.g., Inoue et al., 1987;Takahashi et al., 1993;Ishii et al., 2001;Keeling et al., 2004). By contrast, seasonal variations in pCO 2 sw in the western subarctic zone are dominated by the seasonal variations of DIC associated with the enhanced convection in winter and the large net 15 biological DIC consumption in summer (Takahashi et al., 1993;Tsurushima et al., 2002;Chierici et al., 2006). At interannual to decadal timescales, the dominant mode of basin-scale variability is the Pacific Decadal Oscillation (PDO) (Mantua et al., 1997). Positive PDO anomalies are associated with positive SST anomalies in the Alaskan Gyre and along the west 20 coast of North America, and negative SST anomalies in the central and western North Pacific. While the PDO is expected to impact the distribution of DIC in the upper layers of the North Pacific, the integrated effect of PDO on air-sea CO 2 fluxes remains poorly quantified. Drawing on output from a collection of OBGCMs, McKinley et al. (2006) argued for a correlation of air-sea CO 2 fluxes in the North Pacific with the PDO. Ex-Introduction zone where the ocean is a strong CO 2 sink in winter: inter-annual variations in wintertime pCO 2 sw are rather small, despite sizable interannual variability in SST, because the opposing effects of SST and DIC concentrations on pCO 2 sw compensate each other. This paradigm is consistent with results from the repeated pCO 2 sw measurements in the northern subtropics of the western North Pacific at 137 • E (Midorikawa 5 et al., 2006). This study demonstrated that the inter-annual variations in SST and DIC have a counteracting effect on pCO 2 sw, and consequently the inter-annual variability in air-sea CO 2 flux is thought to be associated with the variability in the wind speed. The modeling study of Doney et al. (2009a) came to the same conclusion (Fig. 3). By contrast, larger amplitude interannual variability in pCO 2 sw and air-sea CO 2 flux in the 10 subarctic zone and in the eastern subtropics are driven primarily by variability in DIC. Long-term trends towards increasing pCO 2 sw have been observed since the early 1980s along a north-south time-series line to the south of Japan at 137 • E (Inoue et al., 1995;Midorikawa et al., 2005Midorikawa et al., , 2012 and at a time-series station near Hawaii (Keeling et al., 2004;Dore et al., 2009). The principal publications to date for basin-scale 15 long-term trends in pCO 2 sw are those of Takahashi et al. (2003Takahashi et al. ( , 2006 and Lenton et al. (2012), which used existing pCO 2 measurements spanning 1970-2004 and from the mid-1990s to the mid-2000s, respectively. These observations show that the mean rate of pCO 2 sw increase is roughly consistent with the rate of atmospheric CO 2 increase, but it is variable both in space and time. Long-term time-series records of 20 oceanic CO 2 appears to show a decrease in the positive trends in pCO 2 sw and DIC in the eastern to southern rim of the subtropical cell and in its tropical branch after the strong warm event of ENSO in 1997-1998(Dore et al., 2003Keeling et al., 2004;Ishii et al., 2009;Midorikawa et al., 2012). A change in the subtropical cell (Qiu and Chen, 2010) is a likely driver, but the mechanism driving a decrease in the rate of Introduction sence of trends in the circulation state of the ocean, and consequently a decadal trend arises towards an increased seasonal cycle. These results found further support in the study of Nakano et al. (2011), who attributed this to the interaction between seasonal dynamics and the changes in carbonate chemistry in seawater with increasing CO 2 . This underscores the importance of accounting for the full seasonal cycle when cal-5 culating long-term trends, as trends inferred from summer-biased measurements will introduce bias in trend estimates (Lenton et al., 2012).

South Pacific extra-tropics
As is the case for the extra-tropical North Pacific, the extra-tropical South Pacific is also a major sink for atmospheric CO 2 . However, this region poses particular challenges to 10 estimating air-sea CO 2 fluxes because of the paucity of pCO 2 sw measurements over this vast sub-basin. The various gridded data products that have resulted from data synthesis activities of pCO 2 sw have by necessity relied on interpolation over large spatial scales and for seasonality in this region. For this region, we may expect that the flux estimates that rely heavily on the pCO 2 sw measurements (namely diagnos-15 tic approaches, pCO 2 sw assimilation, as well as atmospheric CO 2 inversion studies) to exhibit relatively similar mean fluxes, and for estimates that rely either on forward ocean models or ocean CO 2 inversions (which rely more heavily on interior carbon measurements) to produce different time-mean fluxes.

20
We use a range of air-sea CO 2 flux products in the Pacific Ocean, with these products described below. They are mainly the products collected for the Regional Carbon Cycle Assessment and Processes (RECCAP) (Canadell et al., 2011), but they also include products that have been collected in the preparation of this study for the Pacific Ocean synthesis. Introduction

Climatological pCO 2 sw data and pCO 2 sw diagnostic models
The evaluation of the air-sea CO 2 flux through gridded pCO 2 sw data products was originally developed in the studies built on the database of T. Takahashi for shipboard pCO 2 sw measurements (Tans et al., 1990;Takahashi et al., 1997). The database and the gridded data products have been repeatedly updated and widely used since.  (Table 1). A gas transfer velocity (k) is commonly applied to climatological pCO 2 sw data and diagnostic models to estimate the air-sea CO 2 flux employing the following functional 25 form (Sweeney et al., 2007;Park et al., 2012):  (Ardizzone et al., 2009;Atlas et al., 2011). The coefficient 0.25 is specific to the wind-product used to 5 calculate the air-sea CO 2 flux. It has been optimized globally so that the change in the bomb-14 C inventory in the ocean matches atmospheric 14 C invasion rate.
The CO 2 flux (F ) is then calculated by the conventional equation for the bulk method: where C sw denotes the concentration of CO 2 in surface seawater and K 0 denotes CO 2 solubility in seawater at a given temperature and salinity. Following the widely used convention for pCO 2 climatologies and diagnostic models, this flux is positive when CO 2 is released from ocean to the atmosphere and is negative when it is absorbed 15 into the ocean.

Ocean interior CO 2 inversion methods
Ocean interior CO 2 inversion methods use a Green function inverse method to infer regional air-sea CO 2 fluxes from ocean interior DIC observations and ocean general circulation models. This method was first presented by Gloor et al. (2003), and the 20 results shown in this paper are the values of the contemporary flux, i.e., the sum of natural and anthropogenic fluxes presented in Gruber et al. (2009) for the RECCAP period 1990-2009. The inversion was originally done for 30 ocean regions, and then aggregated to 23 regions (10 regions in the Pacific) as described in Mikaloff Fletcher et al. (2006, 2007. These results are generally in good agreement with more recent 25 ocean inverse estimates (Gerber et al., 2009;Gerber and Joos, 2010 Pacific extra-tropics and +0.04 Pg C yr −1 in the tropical Pacific (Jacobson et al., 2007).
The anthropogenic fluxes have been scaled to a 1990-2009 average. A skill score has been determined for each model to account for the substantial differences in the model's ability to correctly simulate the oceanic distribution of passive tracers, and the skill scores are used to calculate the weighted mean net air-sea CO 2 flux (Gruber 5 et al., 2009). Since this method does not resolve seasonal and interannual variability, the results are only used to compare the 1990-2009 mean air-sea CO 2 fluxes.

Ocean biogeochemistry/general circulation models (OBGCMs)
This work also incorporates results from several prognostic ocean biogeochemistry/general circulation model simulations over the period of interest ( Table 2). From a total of nine modeling results, seven were retrieved from the RECCAP website (http://www.globalcarbonproject.org/reccap/products.htm). These simulations include not only an account of seasonally-and inter-annually-varying air-sea fluxes of CO 2 , but also prognostic representations of the processes that are deemed to be important in controlling trends and variations in the ocean carbon cycle. For each case, a prog-15 nostic biogeochemistry model is embedded in a physical ocean circulation model and run online. The surface forcing for the dynamical models consists of using atmospheric flux fields derived from a combination of reanalysis and remotely sensed products. Surface buoyancy forcing is accomplished through the use of bulk formulas or other methods for heat and freshwater fluxes, with a restoring of SSS towards climatological 20 values being characteristic of most of the models. The models considered here are coarse resolution models that are neither eddy permitting nor eddy resolving. Given that the models tend to have differences in their respective (i) underlying physical models, (ii) underlying biogeochemical models, (iii) surface forcing fields, and (iv) handling of river carbon discharge, they should be expected to produce different rep-25 resentations of the ocean carbon cycle. At this point in time, our primary objective will be to provide a description of their similarities and differences. The sensitivity of the Introduction modeled carbon cycle to each of these four differences will not be given any extensive consideration in this study. However, we will be providing at least a preliminary assessment of the sensitivity of the differences in the model results, particularly with respect to the sensitivity of the carbon cycle to physical forcing at the sea surface in Sect. 6.1.

3.4
Ocean pCO 2 sw data assimilation 5 The pCO 2 sw data set of LDEO V2009 has also been assimilated into an offline tracer transport model (OTTM; Valsala and Maksyutov, 2010). This assimilation system minimizes the model biases in the surface ocean pCO 2 through a weak constraint given to its gridded monthly climatology of LDEO V2009, while a strong constraint is given to the in-situ ship-observed pCO 2 sw measurements whenever they are available in the LDEO 10 database (Takahashi et al., 2009b). The weak constraint is further weighted by the inverse of the model interannual variance, which ensures that the model is constrained to the monthly climatological pCO 2 sw only in regions where the interannual variability is small. Assimilated data of pCO 2 sw and air-sea CO 2 flux were constructed from 1996-2008 using this method, while here we present an extended record of the data starting 15 from 1990. Prior to 1996, the data represent the model interannual variability summed to the monthly climatology derived from the assimilation period of 1996-2008.

Atmospheric CO 2 inversion methods
An atmospheric CO 2 inversion intercomparison project community was launched by the TransCom with the RECCAP initiative collecting a number of atmospheric CO 2 inver-  The analysis here includes the inversion results for the Pacific Ocean region from the total of six atmospheric CO 2 inversions with outputs longer than 17 yr for decadal mean flux and ten models for mean seasonal variations (Table 3). It should be noted here that they differ in the atmospheric CO 2 datasets (i.e., observational constraints), atmospheric transport models, spatial resolution of the optimized flux and inversion meth-5 ods. Most of the inversions used climatological air-sea CO 2 flux data from some versions of the LDEO monthly climatology as a prior air-sea CO 2 flux estimate, and therefore regionally-integrated or seasonal variations of posterior net air-sea CO 2 fluxes have been constrained by it to a greater or lesser extent depending on the inversion method.

Regions of assessment
We provide regionally-integrated net air-sea CO 2 fluxes over three sub-basins of the Pacific Ocean that are zonally partitioned. They are the zone to the north of 18 • N including the Bering Sea (< 66 • N), the tropical zone bounded by 18 • N and 18 • S, and the southern zone bounded by 18 • S and 44.5 • S (Fig. 5). The region to the south of 15 44.5 • S is discussed in Lenton et al. (2013). The boundaries separating these three sub-basins are chosen to be consistent with previous publications, grouping 10 prescribed ocean regions of the ocean CO 2 inversions in the Pacific (Mikaloff Fletcher et al., 2006, 2007Gruber et al., 2009). As such, these divisions are fairly consistent with dynamical boundaries separating the subtropical gyres of the North Pacific and to see the effect of westward expansions of the "cold tongue" during the ENSO cold events.
The North Pacific to the north of 18 • N encompasses most of the subtropical gyre and the entire subarctic zone. As shown in Figs. 1 and 2, seasonality of pCO 2 sw reverses within this domain. In winter, pCO 2 sw decreases to considerable CO 2 undersaturation 5 with respect to atmospheric CO 2 in the northern subtropics due to the large effect of seasonal cooling, and pCO 2 sw increases to the point of supersaturation in the subarctic region due to the large effect of DIC increase associated with vertical convection. In contrast, during the summer, pCO 2 sw increases to being in near equilibrium with respect to the atmosphere in the subtropics due to seasonal warming and pCO 2 sw 10 decreases in the subarctic region due to the DIC decrease associated with biological production. The air-sea CO 2 flux shown for the North Pacific extra-tropics is the integrated flux over these two sub-domains. The extra-tropical zone between 18 • S and 44.5 • S covers most of the subtropical gyre in the South Pacific. We note that the southern boundary at 44.5 • S lies in the vicin-15 ity of the Subtropical Convergence Zone and the surface water in this zone is highly undersaturated with respect to atmospheric CO 2 (Metzl et al., 1999;Inoue, 2000;Takahashi et al., 2009a). Therefore, the estimates of air-sea CO 2 flux in the South Pacific extra-tropics is expected to depend largely on the choice of the southern boundary. We will examine this using LDEO V2009 climatological fluxes in Sect. 5.3. 20 For each sub-basin, regionally-integrated air-sea CO 2 fluxes were calculated as monthly means from each product: monthly climatological pCO 2 sw data of LDEO V2009, pCO 2 sw diagnostic models, Ocean BGC models, a pCO 2 sw data-assimilation, and atmospheric CO 2 inversions. Decadal and longer-term mean fluxes were then calculated over the intervals 1990-1999 and 2000-2009, as well as over the combined pe-25 riod 1990-2009. They were subsequently compiled for each of the approaches: the average ± range for pCO 2 sw diagnostic models and the median ± median absolute deviation (MAD) for OBGCMs and atmospheric CO 2 inversions were calculated for decadal and longer-term means. In addition, skill-weighted mean values have been given for BGD 10,2013 Air-sea CO 2 1990-1999 and 2000-2009 in all approaches (Fig. A1). Therefore, in the following sections, we will not mention the decadal means but present only longer-term means for the period 1990-2009 and inter-annual variability and mean seasonal variability for this period. For the pCO 2 sw data assimilation and the atmospheric CO 2 inver-5 sions, mean fluxes were calculated for 1990-2008 since modeling products in the year 2009 were not available. In the cases of pCO 2 sw diagnostic models and OBGCMs, differences in the mean fluxes between for 1990-2009 and for 1990-2008 were minimal (< 0.01 Pg C yr −1 ). Therefore we assume that the comparison of mean and median fluxes for 1990-2009 of diagnostic models and OBGCMs and those for 1990-2008 of 10 pCO 2 sw data assimilation and atmospheric CO 2 inversions are not problematic in the following discussions.

Tropical Pacific 18 • S-18 • N
From the LDEO V2009 climatological pCO 2 sw data set (which has been filtered to re-15 move the ENSO warm events) and CCMP monthly wind speed, the annual CO 2 flux from the tropical Pacific is estimated to be +0.51 ± 0.24 Pg C yr −1 in year 2000 (Table 4; Fig. 6), which comprises a small efflux (+0.06 Pg C yr −1 ) from the western tropical sector (west of 160 • W), and a larger efflux (+0.45 Pg C yr −1 ) from the eastern tropical sector. The mean of the time-averaged air-sea CO 2 flux from the two diagnostic mod-20 els (which include the ENSO warm events) considered here (+0.52 ± 0.09 Pg C yr −1 ) is consistent with the estimates from the climatological pCO 2 sw and the atmospheric CO 2 inversions (+0.53±0.08 Pg C yr −1 ). These diagnostic models also showed a peakto-peak amplitude of inter-annual variability of 0.27 ± 0.07 Pg C yr −1 between 1990 and 2009 ( ical sector during the ENSO strong warm event that occurred in 1997-1998 when the negative anomaly of the flux reached a level of −0.29 and −0.14 Pg C yr −1 , depending on the diagnostic model. This strong warm event was immediately followed by the persistent ENSO cold event in 1998-2000 with quite large positive anomalies in the western sector (up to +0.11 and +0.17 Pg C yr −1 ) as well as in the eastern sector (+0.08 5 and +0.09 Pg C yr −1 ) (Fig. 7). The results of pCO 2 sw data assimilation also shows the inter-annual variability of air-sea CO 2 flux that is associated with the ENSO, although the negative anomaly during the 1997-1998 warm event was smaller (−0.14 Pg C yr −1 ).
The median ± MAD of time-averaged air-sea CO 2 flux in the tropical Pacific evaluated by OBGCMs is +0.39 ± 0.04 Pg C yr −1 for 1990-2009. This is in good agreement 10 with the estimate from ocean interior CO 2 inversion methods (+0.37 ± 0.12 Pg C yr −1 ), but is 0.13 Pg C yr −1 smaller than the estimate from the two diagnostic models considered here. Given the considerable range of flux estimates in both diagnostic models (+0.44 to +0.61 Pg C yr −1 ) and the OBGCMs (+0.25 to +0.55 Pg C yr −1 ), it is important to compare the pCO 2 sw fields and gas exchange coefficients to provide more 15 clarity about these differences. One of the potential sources of the differences is the choice of wind-speed product used to force the ocean circulation in OBGCMs as well as to compute the CO 2 gas transfer velocities that are used both in diagnostic models and OBGCMs. Park et al. (2010) have shown that the global mean air-sea CO 2 flux changes by as much as 20 % with the choice of wind-speed products and coefficient 20 for gas transfer velocity for gas exchange in their diagnostic model. We will discuss this in more detail in Sect. 6.1 for a diagnostic model and for an OBGCM.
In terms of the phase of inter-annual variability, the results from most OBGCMs are consistent with those from diagnostic models demonstrating larger CO 2 efflux during the ENSO cold events and smaller efflux during the warm events. However, OBGCMs 25 appear more sensitive to the ENSO warm and cold events (Table 4 and Fig. 7), particularly during the 1995-1996 cold event and during the 1997-1998 warm event. The reason for the larger ENSO sensitivity in OBGCMs than diagnostic models is yet to be determined but is likely to be attributable to the larger response of the pCO 2 sw field BGD 10,2013 Air-sea CO 2  to these ENSO events. Diagnostic models may more or less smooth out the variability through the regression analyses of pCO 2 sw as a function of SST and other parameters that are used to correct the implicated under-sampling in observations. To date, two modeling studies have evaluated the skill of the diagnostic method originally developed by Lee et al. (1998)

15
The estimates of air-sea CO 2 flux in the tropical Pacific from the atmospheric CO 2 inversions used in this study showed large monthly fluctuations that are not seen in the estimates from diagnostic models and OBGCMs (Fig. 7). Inverse estimates for tropical regions are subject to a high degree of uncertainty due to the limited number of observing stations in this region. Nevertheless, many of the atmospheric CO 2 inverse 20 models show a decrease in outgassing during the strong ENSO warm event in 1997-1998 and an increase during the persistent cold event over 1998-2000. work technique also suggests similar, but slightly smaller, mean influx (−0.40 Pg C yr −1 ) into this domain for the period 2002-2008. This is 0.07 and 0.20 Pg C yr −1 smaller, respectively, than the CO 2 flux estimates from the two other diagnostic models for the same period. Since the same wind product has been used to calculate gas exchange coefficient, these differences in the flux estimate are attributable to the differences in the 5 pCO 2 sw field. The strong CO 2 uptake in the North Pacific is dominated by the uptake in the northern subtropics and subtropical-to-subarctic transition zone in winter (Fig. 2), where the effect of cooling on pCO 2 sw is stronger than the effect of DIC increase due to vertical mixing (Ishii et al., 2001;Takahashi et al., 2002). The mean annual air-sea CO 2 flux in the same sub-basin from pCO 2 sw data assimilation (−0.37 Pg C yr −1 ) is some-10 what smaller, but those from ocean interior CO 2 inversions (−0.42±0.08 Pg C yr −1 ) and atmospheric CO 2 inversions (−0.48 ± 0.08 Pg C yr −1 ) are consistent with the range of estimates from LDEO V2009 climatological pCO 2 sw fields and diagnostic models. The net CO 2 sink estimated by the OBGCMs (−0.57±0.02 Pg C yr −1 ) is the strongest among the estimates from the various approaches.

15
The peak-to-peak difference of the inter-annual variability in the air-sea CO 2 fluxes derived from diagnostic models over the North Pacific extra-tropics is small (0.12 Pg C yr −1 ) ( Fig. 8 and Table 4). This is also the case for the OBGCMs. Most of these models show slightly positive anomalies (∼ 0.1 Pg C yr −1 ) for the period of 1999-2001 when the PDO index tended to be negative, but the relationship between the 20 anomaly of CO 2 flux and the PDO is not discernible for other periods. The amplitude of inter-annual variability is somewhat larger in the flux estimate from pCO 2 sw data assimilation (0.19 Pg C yr With regard to the seasonality of air-sea CO 2 flux in the North Pacific extra-tropics, results from the three diagnostic models are consistent in that they all show very small 5 net air-sea CO 2 flux in summer (July-September: +0.03 ± 0.10 Pg C yr −1 ) and a larger influx into the ocean in winter (January-March: −0.86 ± 0.20 Pg C yr −1 ) (Fig. 9). The difference in the net annual air-sea CO 2 flux among these diagnostic models is mainly attributable to the difference in the flux estimates in the cold time of year (December-April). The phase of seasonality in the pCO 2 sw data assimilation product is consistent 10 with diagnostic models but does shows a net CO 2 efflux in summer (+0.56 Pg C yr −1 in July). All OBGCMs presented in this work also show well-defined seasonality with large CO 2 sink in winter (−1.8 to −0.9 Pg C yr −1 ) and slightly negative or moderately positive flux in summer (−0.1 to +0.6 Pg C yr −1 ). By contrast, in the atmospheric CO 2 inversions large sub-annual variations are found in the air-sea CO 2 flux but its seasonality remains 15 poorly resolved

South Pacific extra-tropics 44.5 • S-18 • S
The climatological net annual air-sea CO 2 flux at the year 2000 evaluated from LDEO V2009 climatological pCO 2 sw was −0.29 ± 0.14 Pg C yr −1 , and the long-term mean net annual air-sea CO 2 flux over two decades after 1990 was −0.28 ± 0.00 Pg C yr Pacific extra-tropics, there is a band serving as a strong CO 2 sink that extends over the mid-latitudes from the region off of Japan to off of the west coast of North America (Figs. 2 and 5). The CO 2 sink is particularly strong around the subtropical-to-subarctic transition zone where the net annual air-sea CO 2 flux from climatological pCO 2 sw of LDEO V2009 reaches −2.9 mol m −2 yr −1 . The western South Pacific extra-tropics near 5 Australia and New Zealand is also a region of CO 2 sink but its strength is moderate (ca. −2.1 mol m −2 yr −1 ). In addition, the eastern South Pacific extra-tropics is a weak sink or even a weak source of CO 2 to the atmosphere. However, it has to be noted that the South Pacific extra-tropics is severely undersampled for pCO 2 sw in winter (Takahashi et al., 2009a) and the uncertainty in the air-sea CO 2 flux is thereby considerably larger sink, the averaged (± standard deviation) flux is −0.71 ± 0.02 Pg C yr −1 , while for the remaining six models a smaller CO 2 sink of −0.32 ± 0.08 Pg C yr −1 is seen, which is more consistent with LDEO V2009 climatology and diagnostic models. The weighted average of net air-sea CO 2 flux from the ocean CO 2 inversions is −0.46 ± 0.10 Pg C yr −1 . This shows nearly a 0.2 Pg C yr −1 larger sink than the estimates from climatological pCO 2 sw and diagnostic models. Only the results from ocean interior CO 2 inversions show a larger oceanic CO 2 sink in the South Pacific extra-tropics than in the North Pacific extra-tropics. 5 With regard to the inter-annual variations, no remarkable change is seen in the diagnostic models (Fig. 8 and Table 4). The estimate from Sugimoto et al. (2012) shows small positive anomalies for 1995-1997 and small negative anomalies for 2006-2008, but they are within ±0.1 Pg C yr −1 . Two of the OBGCMs, i.e., "BER" and "UEA NCEP1"

BGD
( inter-annual variations than the other approaches. This is likely to be attributed to the few data covering land regions in the Southern Hemisphere, such that the atmospheric CO 2 inversions aren't able to effectively distinguish between air-land CO 2 flux and airsea CO 2 flux. Most of the results from the atmospheric CO 2 inversions show large negative anomalies in 1997-1998 (−0.23 Pg C yr −1 on the average) that are larger than 20 the anomalies found in the OBGCMs.

All Pacific Ocean regions 44.5 • S-66 • N
The time-averaged air-sea CO 2 flux for 1990-2009 described in the previous sections reveals a quite large range of variation among the different approaches when integrated over the Pacific Ocean between 44.5 • S and 66 • N ( The results from diagnostic models (−0.27 ± 0.13 Pg C yr −1 ), pCO 2 sw data assimilation (−0.33 Pg C yr −1 ) and atmospheric CO 2 inversions (−0.26±0.10 Pg C yr −1 ) that are more or less constrained by the measurements of pCO 2 sw are consistent with the estimate from the climatological pCO 2 sw. However, the estimate from the ocean interior CO 2 inversions (−0.52 ± 0.18 Pg C yr −1 ) is similar to the results from the OBGCMs. The 5 smaller efflux from the tropics and larger or comparable influxes into the extra-tropics cooperatively contribute to the estimate of larger CO 2 influx into the Pacific from the OBGCMs and ocean interior CO 2 inversions. It is also interesting to note that the efflux from the tropics tends to be balanced by the influx into the North Pacific extra-tropics in the diagnostic models, but it tends to be balanced with the influx into the South Pacific 10 extra-tropics in the estimate from the OBGCMs.
In regard to the inter-annual variability, the diagnostic models and OBGCMs are consistent with each other in that the ENSO-driven change in the tropical zone is playing a dominant role in the Pacific, and changes in the extra-tropics are minor as mentioned in Sects. 5.2 and 5.3 (Fig. 10). In the pCO 2 sw data assimilation and atmospheric CO 2 15 inversions, the inter-annual variability in the air-sea CO 2 flux in the tropical zone is also large, but the effect of ENSO events is less clear.

Dependence of air-sea CO 2 flux upon wind-product
The accuracy of wind field products over the ocean is fundamental to evaluating air-20 sea CO 2 fluxes in all approaches considered in this study. In atmospheric CO 2 inversions, the wind field directly controls the transport of CO 2 . The wind field in the marine boundary layer is also required to drive ocean circulation in the prognostic OBGCMs, the pCO 2 sw data assimilation, and the ocean interior CO 2 inversions. In addition, various gas transfer velocities for CO 2 at the air-sea interface have been given Product (Ardizzone et al., 2009;Atlas et al., 2011). However, it is unclear how the choice of these wind products influences the resultant estimate of air-sea CO 2 fluxes, since a model is usually run with a single wind product and no comprehensive intercomparison exercise has been made in terms of the difference in the wind fields.
In this section, we briefly describe the impact of the difference in wind products on 10 the estimates of air-sea CO 2 flux for a diagnostic model (Sugimoto et al., 2012) and an OBGCM (Buitenhuis et al., 2010). The wind products used here are NCEP/NCAR Reanalysis 1 (NCEP1), which has been often used to force the forward ocean models, and JPL CCMP Ocean Surface Wind Components (CCMP) that we used to calculate the air-sea CO 2 flux with the LDEO V2009 climatological pCO 2 sw and with pCO 2 sw 15 diagnostic models in this work. In the diagnostic model, the gas transfer velocity for CO 2 that was applied in Eq. (1) with the CCMP wind product has a functional form that depends on the monthly mean second moment of wind speed U 2 and an empirical coefficient of 0.25. On the other hand, monthly mean wind speed squared, U 2 , and the coefficient 0.39 has been applied to the CO 2 gas transfer velocity of Wanninkhof 20 (1992) with the NCEP1 wind product. In the OBGCM, daily wind speed and a coefficient appropriate for short term wind speed of 0.3 has been applied with both wind products. Mean seasonal variations and deseasonalized trends of regional mean wind speed, regionally-integrated air-sea CO 2 flux from a diagnostic model (Sugimoto et al., 2012) and that from a OBGCM (Buitenhuis et al., 2010) are shown in Figs. 11 and 12 for 25 each sub-basin of the Pacific Ocean. The seasonality in the regional mean wind speed in the extra-tropics, i.e., stronger in winter and weaker in summer, is clearly seen in Fig. 11. For the inter-annual variability in regional mean wind speed (Fig. 12), a positive anomaly in 1997-1998 in the South Pacific and a trend towards increasing wind speed in the South and tropical Pacific are observed. It is also evident that the mean wind speed in CCMP is always stronger than that in NCEP1. The difference is larger in the tropics (18 • S-18 • N) than in the extra-tropics. In the tropical Pacific, the monthly mean wind speed from CCMP and from NCEP1 varied in parallel to each other, and the time-averaged wind speed over the period 1990-2008 was 6.4 m s −1 in CCMP and 5 5.5 m s −1 in NCEP1. In the North Pacific extra-tropics, no significant difference was seen in the regional mean wind speed in early summer (May-July). However, in winter (December-February), mean CCMP wind speed (8.9 m s −1 ) is 0.6 m s −1 stronger than that of NCEP1. The difference in wind field influences the estimate of air-sea CO 2 fluxes from the and South Pacific extra-tropics, the weaker wind field of NCEP1 rather yielded stronger CO 2 sinks than the stronger wind field of CCMP. The differences are 0.07 Pg C yr −1 for the South Pacific extra-tropics, 0.17 Pg C yr −1 for the North Pacific extra-tropics, and 0.23 Pg C yr −1 when integrated over the sub-basins of the Pacific. These differences in the estimate of regional air-sea CO 2 fluxes due to the use of different combinations 25 of wind field and gas transfer velocity are comparable to, and therefore, may explain a large part of the difference in the estimate between diagnostic models and OBGCMs (Table 4 and Fig. 6) in the extra-tropics and in the entire Pacific. In contrast, the OBGCM of Buitenhuis et al. (2010) that has been forced with the stronger winds of CCMP (Table 2) yielded a stronger CO 2 source in the tropical Pacific and stronger sinks in the extra-tropics than that forced with the weaker winds of NCEP1. The magnitude of inter-annual variability in CO 2 outgassing in the tropical Pacific is also greater when the CCMP wind field was used to force the ocean model. The difference 5 in the integrated CO 2 outflux amounted to 0.22 Pg C yr −1 in the tropical Pacific, and the differences in the integrated CO 2 sinks in the extra-tropics amounted to 0.13 Pg C yr −1 in the South Pacific and 0.09 Pg C yr −1 in the North Pacific. Moreover, it is interesting to note that these differences are offsetting between the tropical source and extra-tropical sinks, and consequently the difference in the flux estimate integrated over the Pacific sub-basins is minor (< 0.02 Pg C yr −1 ). Importantly, the sensitivity described here for one forward OBGCM is likely due to different responses of the subtropical cell overturning to the wind stress component of forcing. For example, if the subtropical overturning strength were to be determined by the strength of the trade winds across 12

BGD
• N and 12 • S, the differences in zonal wind 15 stress at these latitudes could sustain differences in the overturning strength of the subtropical cells, and as a linear advection issue the supply of carbon in the upwelling cold tongue. This may also find expression in increased subduction rates in the extratropical source regions, as illustrated by Fig. 1 of Rodgers et al. (2003). The response of simulated fields of DIC and pCO 2 sw to the different wind forcing would of course 20 vary from OBGCM to OBGCM. However, the results from this model suggest that the smaller CO 2 efflux from the tropical Pacific estimated by the forward OBGCMs than by the diagnostic models (Table 4 and Fig. 6) may reflect not only difference in winds used for calculating gas exchange, but also biases in the dynamical component of the wind forcing for the forward models (surface wind stress).

The "best estimates" of air-sea CO 2 flux in the Pacific regions
A focus of this effort was to obtain "best estimates" of time-averaged net air-sea CO 2 flux in each of the three sub-basins as well as over the entirety of the Pacific Basin by synthesizing the estimates from a variety of approaches. However, it is now clear that the synthesis of the estimates for the air-sea CO 2 flux in the Pacific Ocean does not provide a robust or convincing quantitative path to define a "best estimate". Rather, this synthesis exercise has provided an important first step towards assembling the information that will be needed for future efforts to construct a best estimate. A quantitative assessment building on the results presented here would certainly require skill weighting in the construction of a model-mean or a model-median value 10 of the air-sea CO 2 flux. Although this type of quantitative effort will not be conducted here, we can make loose use of the expression "best estimate" to describe a flux diagnostic that is consistent with what is calculated with the other RECCAP efforts for the other major ocean basins (Schuster et al., 2013;Lenton et al., 2013). This "best estimate" for the air-sea CO 2 flux is taken as the average of the results from (a) the di-15 agnostic models and (b) the ocean interior CO 2 inversions. Both of these approaches are anchored in observational constraints, with the data sources used by these two approaches being independent. As such, this "best estimate" is a simple average of the results obtained with surface pCO 2 sw constraints and results obtained with ocean interior tracer constraints. The uncertainty is then calculated from the uncertainties of 20 the estimate from the diagnostic models (σ dia ) and ocean CO 2 inversions (σ ocn inv ) as riverine carbon discharge has not been taken into account (Table 2), and median ± MAD of flux estimates from all 8 OBGCs were recalculated. In the North Pacific extra-tropics, the "best estimate" thus calculated is −0.47 ± 0.13 Pg C yr −1 . This is consistent with the estimates from the OBGCMs (−0.49 ± 0.02 Pg C yr −1 ) ( Table 4). Good consistency is also seen for the tropical Pacific where 5 the "best estimate" is +0.44 ± 0.14 Pg C yr −1 and the median of the estimates from the OBGCMs is +0.41 ± 0.05 Pg C yr −1 . In the South Pacific extra-tropics, the difference in the estimate of air-sea CO 2 flux between the diagnostic models and ocean interior CO 2 inversions is larger (0.18 Pg C yr −1 ) than those in other regions (0.10 to 0.15 Pg C yr −1 ).
The variation in the estimates among different OBGCMs (−0.39±0.11 Pg C yr −1 ) is also large. However, the mean of the estimates from the diagnostic models and ocean interior CO 2 inversions (−0.37 ± 0.08 Pg C yr −1 ) is comparable to the estimate from the OBGCMs (−0.39 ± 0.11 Pg C yr −1 ). Finally, the "best estimate" of air-sea CO 2 flux for the entire Pacific basins to the north of 44.5 • S (−0.40 ± 0.21 Pg C yr −1 ) was estimated from the results of diagnostic models (−0.27 ± 0.38 Pg C yr −1 ) and ocean interior CO 2 inversions (−0.52 ± 0.18 Pg C yr −1 ). Given the quite large uncertainties and discrepancies between these estimates, it was not possible to obtain estimates with small uncertainty. The estimate for the entire Pacific Ocean basin is in reasonable agreement with the sum of the estimates from the OBGCMs after adding the riverine CO 2 flux (−0.45 ± 0.18 Pg C yr −1 ). 20 Absolutely critical to future efforts to reduce uncertainty in estimating the Pacific carbon sink will be future expansion of the ocean carbon observing system. As we have seen through our synthesis, two central priorities in expanding the observing system should be improving our characterization of seasonal variability and more extensive data sampling of the South Pacific. For pCO 2 sw based flux estimate, an important 25 component of efforts to better estimate CO 2 uptake will involve the combined use of sea surface pCO 2 measurements and diagnostic modeling. Similarly, it will be important to continue collection of hydrographic measurements of CO 2 chemistry given not only their intrinsic value but also their value to ocean inversion efforts. For both cases, the combined data/model analysis in the future will benefit greatly from the implementation and operation of autonomous platforms such as profiling floats and wave gliders mounted with the emerging technology of CO 2 and biogeochemical sensors (e.g., Martz et al., 2010;Fiedler et al., 2013). The autonomous platforms will certainly require coordinated efforts with the accurate measurements and calibration that are provided 5 only by hydrographic measurements from research on oceanographic cruises. Additional measurements can be provided by efforts on voluntary observing ships. It is especially important that measurements are extended to fill in the data gaps in the Pacific Ocean with well considered and planned sampling strategies (e.g., Lenton et al., 2009), particularly in the Southern Hemisphere, and in the seasonal variability.
In addition to the aforementioned monitoring efforts, prognostic ocean modeling will also play an important role in continued development of process-understanding of the controls on physical-biogeochemical coupling in the ocean. As prognostic ocean models are also the basis of both ocean inversion studies and ocean biogeochemical assimilation efforts, they will directly benefit from better process representation in the models used for ocean carbon inversions. As was seen in Fig. 6, the largest discrepancies among the simulations with OBGCMs were found in the South Pacific. We will not identify the underlying cause of the discrepancies in detail within the context of this synthesis, but such discrepancies can result from differences in ocean model resolution, ocean physical parameterizations, and the representation of ocean biogeochemi-20 cal processes. As was seen with the UEA model, important differences can also arise from differences in surface forcing fields.

Conclusions
In this study, a synthesis has been conducted of available observational products and modeling efforts to characterize the air-sea CO 2  given not only to the time-mean fluxes, but also to seasonal variability and interannual variability. With regard to the time-averaged air-sea CO 2 flux for 1990-2009, the estimates from all approaches are consistent in the sign of the flux for the tropical Pacific (efflux) as well as for the extra-tropics of the North and South Pacific (influx) ( Table 4 and Fig. 6). In a considerable number of cases, the regional estimates agree within 5 0.1 Pg C yr −1 . Some larger discrepancies are also seen between different approaches as well as among different models within the same approach.
In the tropical Pacific, time-averaged air-sea CO 2 fluxes over 1990-2009 from ocean interior CO 2 inversions (+0.37 ± 0.12 Pg C yr −1 ) and OBGCMs (+0.39 ± 0.04 Pg C yr −1 ) agree well, but they are smaller than estimates derived from pCO 2 sw diagnostic models (+0.52 ± 0.25 Pg C yr −1 ). Nevertheless the differences are not significant if we consider the 50 % flux uncertainty associated with the gas exchange coefficient and undersampling (Wanninkhof et al., 2013). Since the wind speed in the tropical Pacific has a quite large offset (∼ 1 m s −1 ) among the wind products and the estimate of air-sea CO 2 flux from OBGCMs is considered to be sensitive to the choice of wind prod-15 uct that forces the model, the improvement of wind-speed products could be one of the key issues in reconciling the discrepancies in the flux estimate among these models. For the inter-annual variability, its peak-to-peak amplitude in the OBGCMs (0.40 ± 0.09 Pg C yr −1 ) is larger than that of diagnostic models (0.27 ± 0.07 Pg C yr −1 ). The amplitude is also sensitive to the choice of wind product in the OBGCMs. The 20 skill of the diagnostic models that potentially underestimate inter-annual variability also needs further examinations.
In the North Pacific extra-tropics, where pCO 2 sw diagnostic models and ocean interior CO 2 inversions are relatively well constrained by the data of pCO 2 sw and ocean interior DIC, the agreement of time-averaged air-sea CO 2 fluxes over 1990-2009 be- for pCO 2 sw and ocean interior DIC. The discrepancy in the time-averaged air-sea CO 2 fluxes inferred from the pCO 2 sw diagnostic model (−0.28 ± 0.13 Pg C yr −1 ) and ocean interior CO 2 inversions (−0.46 ± 0.10 Pg C yr −1 ) is larger than in the North Pacific. The discrepancy needs to be reconciled in the future primarily through the increase in measurements both at the surface and in the interior of the ocean. The development of 5 an improved observation network that incorporates deployments of autonomous instruments with CO 2 and biogeochemical sensors has a great potential to contribute to filling in the data gaps in the Pacific Ocean, particularly in the Southern Hemisphere. ics (+0.53±0.08 Pg C yr −1 ), and the South Pacific extra-tropics (−0.29±0.08 Pg C yr −1 ).
The median of the estimates is fairly consistent with the estimate from the LDEO V2009 climatological pCO 2 sw and pCO 2 sw diagnostic models, possibly because of the use of the climatological CO 2 flux from pCO 2 sw in the flux priors.