The OceanFlux Greenhouse Gases methodology for deriving a sea surface climatology of CO2 fugacity in support of air–sea gas flux studies

Climatologies, or long-term averages, of essential climate variables are useful for evaluating models and providing a baseline for studying anomalies. The Surface Ocean CO2 Atlas (SOCAT) has made millions of global underway sea surface measurements of CO2 publicly available, all in a uniform format and presented as fugacity, fCO2 . As fCO2 is highly sensitive to temperature, the measurements are only valid for the instantaneous sea surface temperature (SST) that is measured concurrently with the in-water CO2 measurement. To create a climatology of fCO2 data suitable for calculating air–sea CO2 fluxes, it is therefore desirable to calculate fCO2 valid for a more consistent and averaged SST. This paper presents the OceanFlux Greenhouse Gases methodology for creating such a climatology. We recomputed SOCAT’s fCO2 values for their respective measurement month and year using monthly composite SST data on a 1× 1 grid from satellite Earth observation and then extrapolated the resulting fCO2 values to reference year 2010. The data were then spatially interpolated onto a 1× 1 grid of the global oceans to produce 12 monthly fCO2 distributions for 2010, including the prediction errors of fCO2 produced by the spatial interpolation technique. The partial pressure of CO2 (pCO2 ) is also provided for those who prefer to use pCO2 . The CO2 concentration difference between ocean and atmosphere is the thermodynamic driving force of the air–sea CO2 flux, and hence the presented fCO2 distributions can be used in air–sea gas flux calculations together with climatologies of other climate variables.


Introduction
Observations demonstrate that dissolved CO 2 concentrations in the surface ocean have been increasing nearly everywhere, roughly following the atmospheric CO 2 increase but with large regional and temporal variability (Takahashi et al., 2009;McKinley et al., 2011). In general, tropical waters release CO 2 into the atmosphere, whereas high-latitude oceans take up CO 2 from the atmosphere. Accurate knowledge of air-sea fluxes of heat, gas and momentum is essential for assessing the ocean's role in climate variability, understanding climate dynamics, and forcing ocean/atmosphere models for predictions from days to centuries .
The European Space Agency OceanFlux Greenhouse Gases (GHG) project (http://www.oceanflux-ghg.org/) is an initiative to improve the quantification of air-sea exchanges of greenhouse gases such as CO 2 . The project has developed data sets suitable for computation of gas flux climatology in which mean gridded values are computed from multiple measurements over different years. The gas flux calculation requires accurate values of gas transfer velocity, in addition to the concentrations of the dissolved gas above and below the air-water interface (Liss and Merlivat, 1986). The project has relied heavily on the data sets successfully developed and maintained by the Surface Ocean CO 2 Atlas (SOCAT, Bakker et al., 2014;Pfeil et al., 2013;. SOCAT has collated and carefully quality controlled the largest collection of ocean CO 2 observations providing data in an agreed and controlled format for scientific activities. Recognising that some groups may have difficulty working with millions of measurements, the SOCAT gridded product  was then generated to provide a robust, regularly spaced f CO 2 product with minimal spatial and temporal interpolation. This gridded data set is useful for evaluating models and for studying and characterising f CO 2 variations within regions in a format that is easy to exploit. In this paper we present the OceanFlux-GHG methodology for creating a climatology of f CO 2 suitable for use in air-sea gas flux studies. Gas concentrations of CO 2 in the upper ocean can be derived from SOCAT's underway sea surface measurements of fugacity, f CO 2 (p CO 2 adjusted to account for the fact that the gas is not ideal regarding molecular interactions between the gas and the air). The aquatic CO 2 concentration can be expressed as the product of f CO 2 and solubility of CO 2 ; the product of CO 2 concentration difference and gas transfer velocity, k, then gives us the air-sea gas flux. Different authors of CO 2 ocean-atmosphere gas flux products use either a mean value of f CO 2 (e.g. Schuster et al., 2009; or p CO 2 (e.g. Takahashi et al., 2002Takahashi et al., , 2009Landschützer et al., 2013;Jones et al., 2012;Rödenbeck et al., 2013) within a grid box for a particular measurement month and year. Many studies have used the p CO 2 climatology of Takahashi et al. (2002Takahashi et al. ( , 2009) as a basis to estimate their own air-sea fluxes (e.g. Kettle et al., 2005Kettle et al., , 2009Fangohr and Woolf, 2007;Land et al., 2013). The data sets from Takahashi et al. (2002Takahashi et al. ( , 2009) and Sabine et al. (2013) are calculated using in situ SST obtained at depth, SST depth . In situ f CO 2 is derived from f CO 2 measured in the shipboard equilibrator using the difference between the temperature of sea water in the equilibrator and SST depth . Because f CO 2 is highly sensitive to temperature fluctuations, an instantaneous measurement of f CO 2 is only really valid for its concurrent in situ SST depth measurement. Takahashi et al. (2009) note there is a bias between the temperatures associated with the partial pressure measurements (and their gridded and interpolated values) and the SST depth product used in their calculation of solubility (and thus fluxes). That inconsistency implies a bias between the upper ocean p CO 2 values with the true climatological mean values. They estimate a mean +0.08 • C temperature difference, introducing a systematic bias of about +1.3 µatm in the mean surface water p CO 2 over all monthly mean values obtained in their study. They apply a correction to the global CO 2 flux on that basis. Takahashi et al. (2009) also acknowledge that by using SST depth in their calculations, surface-layer effects could introduce systematic errors in the sea-air p CO 2 differences. Additional SST biases are also likely introduced by different measurement systems that measure SST at sea (Donlon et al., 2002), each with their own characteristic measurement biases.
All biases in SST, and hence in f CO 2 , contribute to uncertainties in the true monthly means of f CO 2 . Also for the purposes of calculating fluxes, each grid-cell value of fugacity must be paired with a SST value, such that temperature products are used consistently and correctly throughout the flux calculation. A true monthly mean value of f CO 2 should therefore be estimated by calculating f CO 2 for a monthly mean value at a consistent SST appropriate to the gas flux calculation. As explained in detail below, we use a representative, accurate and consistent value of SST for each grid-cell value of f CO 2 .
The focus of this paper is to critically assess f CO 2 calculations and the application of f CO 2 for CO 2 ocean gas flux climatology development, with an emphasis on the need to properly address inconsistencies in SST measurement methods. In other respects, we use simple approaches to the calculation of a climatology (for example, simple geospatial interpolation). We first review the importance of SST to the calculation of f CO 2 and the use of satellite SST data. We then review the monthly composite SST data that we derived from SOCAT's regional synthesis files and compare those to satellite observations of SST. In Sect. 2 we briefly describe the SOCAT data set and methods, followed by an explanation of our approach to compute a climatological f CO 2 from the SOCAT in situ f CO 2 data (Sect. 3). In Sect. 4 the spatial interpolation using ordinary block kriging is detailed and in Sect. 5 the resulting f CO 2 climatology and a range of possible errors are discussed. Our application of the recently released SOCAT "version 2" data set is the subject of Sect. 6. The month January is used as an illustrative example of the data treatment throughout this paper. In the conclusion (Sect. 7) SOCAT version 1.5 and 2 and their uses are compared and a recommendation for future versions of SOCAT is given.
In this paper, we explain the reasons for our conversion of f CO 2 for in situ SST to f CO 2 for monthly composite SST from satellites and the methodology of our conversion in detail. The resulting data sets are useful for air-sea gas flux studies and are given as a supplement to this publication. We will not interpret the oceanographic features that can or cannot be distinguished in our maps. We leave that to continuing work within and beyond the OceanFlux-GHG project.

Complexities of in situ SST measurements and implications for f CO 2
As already discussed, f CO 2 is highly sensitive to temperature. Similarly, accurate knowledge of SST and, to a lesser extent, salinity, is essential when calculating air-sea gas fluxes. SST vertical profiles are complex and variable. SST can also vary over relatively short time scales within relatively small regions and variations in the temperature measured can also arise from the method and instrumentation used for measur- Figure 1. A schematic of the surface ocean, depicting the definition of the mass boundary layer (MBL), thermal skin and temperatures at various depths (Donlon et al., 2002). SST depth can be from centimetres to metres below the surface, but is commonly around 5 m in the SOCAT data.
ing it. All of these issues can cause problems when using in situ data to construct a f CO 2 climatology. These issues are now discussed. We begin with issues surrounding individual measurements of SST and then consider the quality of composite values of in situ derived SST (i.e. averages over a defined grid cell). The structure of the upper ocean (∼ 10 m) vertical temperature profile depends on the level of shear-driven ocean turbulence and the air-sea fluxes of heat, moisture and momentum. Every SST observation depends on the measurement technique and sensor that is used, the vertical position of the measurement within the water column, the local history of all components of the heat flux conditions and, the time of day the measurement was obtained (Donlon et al., 2002). The subsurface SST, SST depth ( Fig. 1), will encompass any temperature within the water column where turbulent heat transfer processes dominate . Such a measurement may be significantly influenced by local solar heating, the variations of which have a time scale of hours, and typically temperature will vary with depth. Diurnal warming and the formation of a "warm layer" may occur at the sea surface when incoming shortwave radiation leads to stratification of the surface water. In the absence of windinduced mixing, temperature differences of > 3 K can occur across the surface warm layer (Ward et al., 2004), which in turn will enhance the outgassing flux of CO 2 (Jeffrey et al., 2007(Jeffrey et al., , 2008Kettle et al., 2009). In order to address such issues, the international Group on High Resolution Sea Surface Temperature (GHRSST) states that SST depth should always be quoted at a specific depth in the water column; for example, SST 5 m refers to the SST at a depth of 5 m. However, SST depth data can be measured using a variety of different temperature sensors mounted on buoys, profilers and ships at any depth beneath the water skin and the depth of the measurement is often not recorded. Different measurement systems that are used to measure SST (e.g. hull mounted thermistors, inboard thermosalinograph systems) have evolved over time using different techniques that are prone to different error characteristics (e.g. for a good review see Kennedy, 2013;Kennedy et al., 2011a, b), such as warming of water as it passes through the ships' internal pipes before reaching an inboard thermosalinograph (e.g. Kent et al., 1993;Emery et al., 2001;Reynolds et al., 2010;Kennedy, 2013), poor calibration or biases due to the location and warming of hull mounted temperature sensors (e.g. Emery et al., 1997Emery et al., , 2001, inadequate knowledge of temperature sensor depth (e.g. Emery et al., 1997;Donlon et al., 2007), poor knowledge of temperature sensor calibration performance and local thermal stratification during a diurnal cycle (e.g. Kawai and Wada, 2007). This means that if not carefully controlled, SST biases of > 1 K may easily be introduced into an in situ SST data set.
An additional set of issues surrounds the calculation of gridded values of SST derived from in situ data. Here, in addition to potential biases in individual measurements, we should consider whether the sampling by in situ methods is sufficient. In respect to the SST measurements paired to CO 2 measurements, there is an issue (Takahashi et al., 2009), which is likely to result from a combination of undersampling, temperature gradients and measurement bias.
All of these issues mean that directly using SST and f CO 2 measurement pairs from a large data set (i.e. that resulting from a large number of different instrument set-ups and methods) for a f CO 2 climatology for studying air-sea gas fluxes is likely to introduce errors. In summary, three steps must be achieved to estimate true monthly mean values of f CO 2 to (1) adjust for errors due to the vertical SST gradient, (2) minimise the bias due to undersampling (related to grid-box averaging of the measurement data), and (3) minimise errors due to the different methods and instrumentation. Therefore, we propose that correcting all of the f CO 2 data back to a consistent surface SST data set is clearly advantageous, and this is where satellite data can be useful.

The use of satellite sea surface temperature data
Satellite Earth observation thermal infrared radiometers have been in orbit around the Earth since the 1990s and global SST products based on these instruments are available. The radiometers are sensitive to thermal radiation from the "radiometric skin" of the ocean and more recent products are calibrated exclusively against other "skin SST" measurements (rather than SST measurements at depth). In addition to individual measurements, composite or gridded values of SST are calculated and these have a low sampling uncertainty for monthly values. These satellite products have been shown to have a higher accuracy and precision for studying SST than in situ methods (e.g. O'Carroll et al., 2008) and such data are now available as a climate data record (Merchant et al., 2008(Merchant et al., , 2012. We used satellite derived SST values from the Along Track Scanning Radiometers, ATSRs, Reprocessing for Climate project, ARC (Merchant et al., 2012). This climate data record is a global, long-term, homogenous, highly stable SST data set based on satellite-derived SST observations.
We have mentioned thermal gradients within the upper metres of the ocean, and particularly warm layers, in the previous section, but it is also important to note that the very surface of the ocean and the radiometric skin are typically one to two tenths of a Kelvin cooler than the water millimetres below, due to cooling at the sea surface and limited eddy transport within the top millimetre of the ocean. Thus, a thermal skin is defined as shown schematically in Fig. 1. The low eddy transport also affects gas transport and a mass boundary layer, MBL (Fig. 1), is defined for air-sea gas exchange. Though both the thermal skin and MBL are products of limited eddy transport, MBL is thinner than the thermal skin due to the lower molecular diffusivity of dissolved gases. The concentration difference across MBL is the driving force behind the air-sea flux of CO 2 . A calculation of the concentration difference requires attention to vertical thermal gradients both in the top millimetre and in the several metres below. As discussed previously, in situ subsurface seawater fugacity is normally measured several metres below the surface. The direct application of these measurements for deriving air-sea fluxes (e.g. Takahashi et al., 2009) implicitly assumes that the measured fugacity values at depth are the same as those at the bottom of the MBL. The formation of warm layers will certainly undermine this assumption and the thermal skin adds a significant additional complication. Satellites directly provide a radiometric temperature virtually equivalent to the temperature at the top of the thermal skin and MBL. At wind speeds of approximately 6 m s −1 and above, the relationship between SST skin (at the top of the skin) and SST subskin (Fig. 1) is well characterised for both day-and night-time conditions by a cool bias (e.g. Donlon et al., 2002). Therefore a skin temperature value from Earth observation with an appropriate correction for the cool skin bias can be used to describe the temperature at the base of the thermal skin, thus avoiding the effects of warm layers and other thermal gradients below the skin. Temperatures within the thermal skin (for example, defined for the base of the MBL) are not a standard product, but could also be estimated from SST skin . There are some remaining ambiguities regarding precisely which satellite-based temperature product is optimal for generating a climatology, but any temperature calculated from composite satellite derived SSTs is preferable (to calculate composite values of CO 2 parameters at the base of the MBL) in comparison to an in situ SST depth product. The practical differences between satellite and in situ temperature products are described in the next section.

A comparison between SST data sets
In air-sea gas flux calculations, an estimate of the water side f CO 2 , and hence the temperature, is required at the base of the mass boundary layer. However, ARC SST data are measurements of the sea surface skin, SST skin , which is char- acteristically cooler than the water just below it. Since gas transfer velocities are low in low wind speeds, it is more important to have a reasonably accurate estimate of the thermal skin effect in moderate and high wind speeds. Donlon et al. (1999) reported a mean cool skin T = 0.14 (±0.1) K for wind speeds in excess of 6 m s −1 and so we used this to derive SST subskin (the SST at the base of the thermal boundary layer, Fig. 1) from ARC SST skin .
The ARC data set provides daily day-time and night-time averages of SST skin (K) from infrared imagery gridded to a 0.1 • latitude-longitude resolution (Merchant et al., 2012). For each year from 01 August 1991 to 31 December 2010, we calculated the monthly mean SST skin distributions, averaged over a 1 • × 1 • grid without differentiating between day-and night-time measurements (http://www.oceanflux-ghg.org/Products/OceanFlux-data/ Monthly-composite-datasets). These SST skin grid points were linearly interpolated to the ith SOCAT measurement location (SST skin,i ). We defined T ym (K) as the 1 • × 1 • grid box mean of T ym,i = SST skin,i + 0.14 K in the measurement year "y" and measurement month "m". The f CO 2 values were then re-computed from in situ SST to satellite T ym,i for our climatology (Sect. 3.2).
Using 1 • × 1 • grid box means of the difference between T ym,i and SOCAT's instantaneous in situ SST measurement (generally obtained at 5 m nominal depth) converted to unit K and all data from the years 1991 to 2007, a histogram of dT = T ym − SST (K) was produced (Fig. 2). It shows that dT was distributed around a median and mean of −0.09 K with a standard deviation of 0.55 K. Assuming the cool skin effect has been corrected accurately, this difference implies L. M. Goddijn-Murphy et al.: The OceanFlux Greenhouse Gases methodology 523 that the gridded in situ SST systematically overestimated T ym (our estimate of SST subskin ). The corresponding histogram of 1 • × 1 • grid box means of the difference between f CO 2 converted to a monthly composite and the original SOCAT's in situ f CO 2 (df CO 2 = f CO 2 (T ym ) − f CO 2 ) using data from all years (not shown) revealed a similar distribution with a mean of −1.21 µatm and standard deviation of 9.36 µatm. The temperature differences were found to be positive as well as negative (Fig. 2). Positive dT can be a consequence of diurnal warming when the top layer heats up by solar radiation during the day. This heat is lost again during the night. Cooling of the top layer (negative dT ) is a less described phenomenon but can be expected in colder environments. Alternatively, it is possible that negative dT results because the in situ data are biased warm, perhaps because the warming before reaching a ship-board thermosalinograph is systematically underestimated. We found more negative dT during the winter months and at high latitudes. The temperature profile in the sea depends on wind speed as wind mixes the water column, i.e. for strong winds SST is expected to be more constant in the vertical. Figure 3 illustrates the wind speed dependence of dT for the North Atlantic. This region was chosen because it has the highest SOCAT data density. For each dT we retrieved the monthly 1 • × 1 • grid box mean of 10 m wind speed, U 10 (m s −1 ), using the Oceanflux-GHG's composite of GlobWave merged altimeter wind speed data (http://www.oceanflux-ghg.org/Products/ OceanFlux-data/Monthly-composite-datasets). The scatter plot of dT as a function of U 10 , averaged over in 1 m s −1 U 10 bins, (Fig. 3) shows that dT decreased with increasing U 10 becoming negative for wind speeds over about 10 m s −1 . Similar trends were seen in the other regions, but with dT turning negative for different wind speeds: North Pacific 9 m s −1 ; Coastal 8 m s −1 ; Tropical Atlantic and Southern Ocean 6 m s −1 ; Tropical Pacific, Indian Ocean and Arctic 4 m s −1 . The Tropical Atlantic was different in that dT became less negative for wind speed over ∼ 8 m s −1 , turning positive over ∼ 10 m s −1 . If only North Atlantic data from the winter months December, January and February were included, nearly all dT values were negative. The analyses of SST differences described above, suggest strongly that the original in situ temperatures are biased and that bias varies spatially and seasonally. Therefore, a correction of CO 2 parameters for temperature is appropriate.

Corrections of f CO 2 for SST
Having concluded that the temperature originally paired with a CO 2 measurement is not suitable for a gridded air-sea flux calculation, we require a guiding principle to calculate "revised values" that can be paired with consistent and appropriate SST values throughout the flux calculations. The principle that we apply is that for changes in temperature within each grid cell, the fugacity changes can be calculated to a good approximation by assuming the changes in the carbon- . Scatter plot of temperature difference (K) between monthly gridded data of subskin SST derived from ARC, T ym , and in situ SST from SOCAT version 1.5, using data from all available years in the North Atlantic, binned in 1 m s −1 U 10 bins. The error bar indicates the standard error of the mean.
ate system are isochemical. That principle is standard for corrections within a measurement system (for example where the sample water is warmed between collection and measurement in an equilibrator) and can also be applied with some confidence to the changes effected by warm layer formation and destruction (Olsen et al., 2004;Jeffery et al., 2007). Applying the principle more broadly is less satisfactory, but given the value of calculating consistent and robust values of temperature and carbonate parameters for air-sea flux calculations, it is a reasonable action. Essentially, we assume that there will not be systematic sample biases in alkalinity or total dissolved inorganic carbon within the grid cell, but the original temperatures may be poorly measured, poorly sampled or affected by vertical temperature gradients. Dissolved inorganic carbon is partitioned between dissolved gas, bicarbonate ions and carbonate ions and the fractions of each is temperature dependent. An isochemical change in the system changes the concentration and fugacity of the dissolved gas without altering the alkalinity or the total dissolved inorganic carbon. In Sect. 3, we describe the recalculation of fugacities and partial pressures by applying this principle.
An important subtlety is that we recalculate fugacity at SST subskin rather than the theoretical temperature at the base of MBL. Some of the reasons are simply pragmatic: e.g. calculating SST subskin is quite standard and the correction to composite values of this temperature achieves the primary objective, since the temperature difference with in situ temperatures (Figs. 2 and 3) is generally larger than those within the thermal skin. Another reason is theoretical: the response time of the carbonate system is limited by the hydration reaction and it is unlikely that substantial repartitioning (and changes in the concentration of the dissolved gas) will oc-cur between the base of the thermal skin and the base of the MBL. Therefore a concentration calculated from the solubility and fugacity at SST subskin should also be appropriate for the base of the MBL.
An overview of all the different parameters used in our re-computation is presented in Appendix A1. The SOCAT measurements and methods are described in Sect. 2 and Appendix A2 and our re-computation in Sect. 3 and Appendix A3.

The SOCAT database
The SOCAT database contains millions of surface-ocean CO 2 measurements in all ocean areas spanning four decades (Bakker et al., 2014;Pfeil et al., 2013). All data are put in a uniform format, while clearly defined criteria are applied in their quality control. SOCAT has been made possible through the cooperation (data collection and quality control) of the international marine carbon science community. The history and organisation of SOCAT is described in Pfeil et al. (2013). SOCAT version 1.5 includes 6.3 million measurements from 1968 to 2007 and was made publicly available in September 2011 at http://www.socat.info/SOCATv1/. SOCAT data are available as three types of data products: individual cruise files, gridded products and merged synthesis data files. For our study we used the latter and we downloaded the individual regional synthesis files from http://cdiac.ornl.gov/ftp/ oceans/SOCATv1.5/. The content of these files (parameter names, units and descriptions) are described in Table 5 in Pfeil et al. (2013). The data can be displayed in the online Cruise Data Viewer (Fig. 4) and downloaded in text format. More recently, on 04 June 2013, the updated database SO-CAT version 2 was released containing 10.1 million surface water f CO 2 values (Bakker et al., 2014). Additional data are from cruises during the years 2008 to 2011, from the Arctic, and previously unpublished data from earlier cruises. Also the quality control is tightened and some data has been removed.

Measurements of p CO 2 (T eq )
The measurement method of p CO 2 in seawater described by Takahashi et al. (2009) is summarised in the following. On board the ship a head space of an equilibrator is equilibrated with streaming seawater and the concentration of CO 2 in the equilibrated carrier gas is measured. When a dry carrier gas is analysed, seawater p CO 2 (T eq ) in the equilibrator chamber at temperature T eq is computed using where P eq is the pressure at the equilibrator (atm), P w water vapour pressure (atm) at T eq and salinity (S), and x CO 2 ,dry the mole fraction of CO 2 in dry air (ppm) for p CO 2 in µatm. P w (atm) is calculated with with T eq in K . When mixing ratios in a wet carrier gas (100 % humidity) are determined, P w is absent

Temperature handling
There are different methods to correct for the difference in partial pressure at intake and equilibrator temperature. SO-CAT uses the simple Eq. (A1) . Takahashi et al. (2009) note that a more complicated formula is more accurate, with SST and T eq in • C. Equations (A1) and (4) correct for the effect of slight warming before measurement at the equilibrator in an isochemical transformation. Equation (4) is an integrated form of (4) should be slightly more accurate, but it can be shown that the simpler form will not be a major source of bias in p CO 2 ,is estimates.

Our re-computation for climatological fugacity in the year 2010
In our re-computation of f CO 2 for SOCAT's in situ SST to monthly composite f CO 2 we only used "good" records (WOCE_flag = 2) with valid f CO 2 ,is and SST. Our recomputation required multiple steps (see Appendix A1 for definitions of variables): 1. estimate original p CO 2 measurement at T eq ; 2. convert p CO 2 (T eq ) to p CO 2 (T ym,i ); 3. calculate f CO 2 (T ym,i ) from p CO 2 (T ym,i ); 4. apply linear trend to extrapolate f CO 2 (T ym,i ) and p CO 2 (T ym,i ) to year 2010; 5. bin the data by month and in 1 • × 1 • grid boxes; 6. spatially interpolate the grid boxes.
The first three steps were necessary because mole fraction x CO 2 ,is , and partial pressures p CO 2 ,is and p CO 2 (T eq ) are not given in the SOCAT regional synthesis files (so Eqs. A2 and 4 could not be used directly to calculate f CO 2 ,ym,i ). The first step of estimating the original measurement of p CO 2 (T eq ) is described in Appendix A3. Note also that by first returning to the partial pressure at the equilibrator temperature, any measurement bias in the in situ temperature is removed thereafter. If T eq was not given we skipped step 1 and used SST to convert p CO 2 (SST) to p CO 2 ,ym,i in step 2; those records will carry the effect of any measurement bias in the in situ temperature into the recalculated values. The next step was to convert partial pressure at equilibrator temperature to partial pressure at T ym,i for each SOCAT measurement. Because ARC ATSR data were available from 01 August 1991 we converted SOCAT data from 01 August 1991 until 31 December 2007. As a consequence 95249 (1.4 %) of valid f CO 2 observations were not used from the SOCAT v1.5 data set (from 119 cruises spread all over the globe). We note that the ESA SST Climate Change Initiative (CCI) project is now working on an extended SST climate data record from satellite extending back to 1981, which is expected to be made available in 2015. We used Eq. (4) to correct for the difference between monthly composite and equilibrator temperature in • C resulting in p CO 2 ,ym,i = p CO 2 (T eq ) exp 0.0433(T ym,i − T eq ) − 4.35 × 10 −5 (T 2 ym,i − T 2 eq ) The subscript "ym" indicates a "single year monthly composite" and "i" interpolated to SOCAT sample location (Sect. 1.4). As explained in Sect. 1.5, Eq. (4) was applied on the basis that an isochemical transformation between SST and T ym is a reasonable assumption. In a third step, monthly composite estimations of f CO 2 ,ym,i (µatm) were calculated from p CO 2 ,ym,i by inverting Eq. (A2), with B = B (CO 2 , T ym,i ) (Eq. A3) and δ = δ (CO 2 , T ym,i ) (Eq. A4) and temperatures in K. We estimated P eq,ym from sea level pressure estimated at closest grid value from 6 hourly NCEP/NCAR as given in SOCAT's merged synthesis files (ncep_slp in hPa). To account for the overpressure that is normally maintained inside a ship 3 hPa was added (P eq,ym = ncep_slp + 3 hPa) (Takahashi et al., 2009) and P eq,ym was converted to unit atm. Note that we recomputed SOCAT's f CO 2 for monthly composite SST and atmospheric pressure, but not for monthly composite salinity. Finally, the f CO 2 ,cl,i and p CO 2 ,cl,i data were grouped by month and averaged over 1 • × 1 • squares. Not all 1 • × 1 • grid boxes were filled and we horizontally interpolated between filled values to produce global p CO 2 ,cl and f CO 2 ,cl distributions (Sect. 4).

Horizontal extrapolation using ordinary block kriging
Unlike Takahashi et al. (2009), our climatology includes data from El Niño years and coastal locations. We added p CO 2 ,cl for those who prefer to use partial pressure; p CO 2 ,cl levels were slightly higher (less than 2 µatm) than f CO 2 ,cl . For the spatial interpolation of the gridded data on a 1 • × 1 • mask map of the global oceans, we used the variograms and kriging options within gstat, which is an open source tool for multivariable geostatistical modelling, prediction and simulation (gstat home page: http://www.gstat.org/). Gstat finds the best linear unbiased prediction (the expected value) with its prediction error for a variable at a location, given observations and a model for their spatial variation (Pebesma, 1999(Pebesma, , 2004. We used the "ordinary block kriging" option. We quantified the prediction error as standard deviation, SD (square root of the variance given by gstat). As would be expected, the prediction errors were large in areas with data sparsity. First, we modelled the variogram for f CO 2 ,cl for each month using gstat's interactive user interface (Pebesma, 1999(Pebesma, , 2004. A variogram describes how the data vary spatially and can be represented by a plot of semivariance against distance. The variograms best fitted combinations of a nugget and a spherical model, a Nug(0) + b Sph(c), and for each month variogram parameters a, b and c were derived (e.g. Fig. 5). Figure 5 shows that at small separation distances, the semivariance in f CO 2 (computed as one-half of the difference in f CO 2 squared) is small, so that points that are close together have similar f CO 2 values. After a certain level of separation (c), the variance in the f CO 2 values becomes rather random and the model variogram flattens out to a value corresponding to the average semivariance (a + b). The model variogram is used to compute the weights used in the kriging. The variogram coefficients were different for each month because each monthly data set had a different data distribution. The fitted variogram models were applied in the kriging of both f CO 2 ,cl and p CO 2 ,cl because the difference with f CO 2 ,cl was negligible compared to the spatial variation. By using the variogram to compute the weights for the interpolation, the expected estimation error is minimised in a least squares sense so that the kriging produces the best linear unbiased estimate.
We applied ordinary kriging on mask map locations because it is the default action when observations, variogram, and prediction locations are specified (Pebesma, 1999). We performed local ordinary block kriging directly on a 1 • × 1 • mask map of the global oceans with minimum (min) of 4, maximum (max) of 20, and radius of 60 • . Thus, after selecting all data points at (euclidian) distances from the prediction location less or equal to 60 • , the 20 closest were chosen when more than 20 were found and a missing value was generated if less than 4 points were found. It should be noted that the interpolation did not necessarily stop at land barriers in areas with few or no data points. Also the decorrelation length was most likely shorter than 60 • kriging radius for the majority of the grid cells .  do not show that changes in surface-ocean p CO 2 are larger in either the east-west direction or the north-south direction. We had to choose between a small kriging radius and generating a few high-quality grid cells but many empty grid cells, or a large kriging radius and generating few empty grid cell values but many with high SDs. We chose the latter in order to produce almost complete maps and with the option that a quality filter could be applied later. The data were smoothed by averaging over square shaped 5 • × 5 • sized blocks. Thus gstat produced the f CO 2 ,cl (and p CO 2 ,cl ) prediction and variance values located at the grid cell centres of the (non-missing valued) cells in the grid map mask. These results were compared with results from different kriging options min, max, radius and block size (Sect. 5.3).
Our approach to the interpolation of these sparse data is simpler and more straightforward than other previous methods. This choice was deliberate as optimal interpolation of such sparse environmental data is itself a focus of international research. For example, the spatial interpolation on a 4 • × 5 • grid of Takahashi  × 5 • grid using sub-annual δp CO 2 / δ SST trends and inter-annual SST anomalies.

Monthly global maps
The prediction distributions of f CO 2 ,cl produced by the ordinary block kriging are shown in Fig. 6 for January; Fig. 7 shows the associated standard deviations and Fig. 8 the f CO 2 ,cl predictions with high prediction errors (SD > 25 µatm) masked. Grid-box values, as shown in Fig. 8 for January, were averaged over 3 months (an empty grid box was generated if it did not contain at least one valid value with SD < 25 µatm) resulting in four seasonal distributions of f CO 2 ,cl (Fig. 9). The 12-monthly global distribu- tion data have been made available in 12 NetCDF files in the supplement related to this article. These files contain f CO 2 ,cl , p CO 2 ,cl , their kriging errors, and ARC's SST skin for the year 2010, all on a 1 • × 1 • grid. The variable names are respectively f CO2_2010_krig_pred, pCO2_2010_krig_pred, f CO2_2010_krig_std, pCO2_2010_krig_std, and Tcl_2010 (T ym as defined in Sect. 1.4 for the year 2010). Also given is vCO2_2010, the mole fraction of CO 2 in dry air (ppm) in 2010 from the Earth System Research Laboratory of the National Oceanic and Atmospheric Administration, NOAA ESRL, (Dlugokencky et al., 2014) on the 1 • × 1 • grid. This variable is not used in our re-computation, but is included because it is used in air-sea flux calculations. The important differences with the Takahashi climatology are summarised in Table 1. A comparison between the Takahashi climatology, normalised to the year 2010 by adding 15 µatm (= 1.5 µatm yr −1 × 10 y), and OceanFlux p CO 2 ,cl is shown in Fig. 10. The general distribution is similar with large differences mainly confined to poorly sampled regions such as the Arctic and some coastal zones. For the wellsampled zone 14-50 • N in the North Atlantic and North Pacific, the climatologies are satisfactorily similar, with the discrepancies of the respective seasonal p CO 2 ,cl averages being less than ∼ 2.4 and ∼ 4.4 µatm ( Table 2), but there are some interesting if subtle differences. For instance, both products exhibit a seasonal signal in the North Atlantic but the amplitude of that seasonal signal is noticeably stronger in the new product (thus positive difference in summer, negative difference in the winter).
Differences with Takahashi and other climatologies arise for four key reasons.
1. The selection of data. Our product relies on quality control within SOCAT and should in this respect be comparable to other products derived from SOCAT, but may differ significantly from Takahashi et al. (2009) for which the selection of data is less transparent. 2. The handling of temperature. Our methods differ substantially from those used previously. As explained earlier, we are convinced our handling is more rational and consistent with the eventual calculation of fluxes. Though the mean difference in temperature is fairly small, we have noted already that some regional and seasonal differences are large.
3. The interpolation methods. We have deliberately used a very simple interpolation method based on block kriging. As shown by Figs. 7 and A4, the resulting standard deviations are large and the appearance in poorly sampled regions and seasons is poor. These sparsely sampled regions are not the only regions that show some very obvious differences with Takahashi, for example the eastern-central equatorial Pacific. Other methods produce superficially more pleasing results in the sparsely sampled regions, but they rely on relationships with other variables (e.g. circulation or temperature) that may or may not be robust.

4.
The reference year and assumed secular trends. These are clearly significant, but the sensitivity to secular trends in oceanic p CO 2 will need to be investigated in a later study.
Calculating all errors is difficult, but we considered the following errors. The prediction errors were estimated by taking the square root of the variances of the kriging. The different kriging approaches themselves were evaluated by calculating the mean and standard deviations of the varying f CO 2 ,cl kriging results using the options shown in Table 3. The specific timing and path of ship tracks can affect the results. Therefore we used a bootstrapping approach to investigate if certain cruises dominated the mapped results. Other errors that were analysed were the "temporal extrapolation error", the "inversion error" related to the different starting points of the conversion, the consequences of the absent values in our recomputation, and the propagations of the uncertainties in the SOCAT measurements and T ym,i . These errors are discussed in the next sub sections and the final subsection gives a summary overview.

Spatial interpolation errors
The standard deviations (SDs) of the prediction produced by the kriging were calculated by taking the square root of the variance values produced by gstat (Pebesma 1999). These prediction errors were related to the available SOCAT data density in each measurement month (e.g. Figs. 4 and 7) and also to errors in the grid point values of f CO 2 ,cl themselves as they are propagated in the kriging operation. For each month we calculated the global mean, min and max of the SD. Over the 12 months, the monthly SD over all grid points was 20 ± 5 µatm on average (mean over all monthly means ± SD of the mean). The average monthly minimum/maximum SD values were 6.3 ± 2.6/50 ± 8.7 µatm (mean over all monthly min max values ±SD of the mean). Areas with large SD emerged where no SOCAT data were available, for example in the western Southern Ocean and the Arctic. Spatial interpolation errors were lowest in the North Atlantic and North Pacific where SOCAT data was densest. The month April showed the highest errors, this could be a consequence of the variogram range, c, being the smallest, implying that the covariance between the locations dropped quickly with distance In other words, the spatial autocorrelation length was short in April (24 • ), indicating that f CO 2 was spatially less stable in April , and the consequent error was recognised by the kriging method. Our variogram model of combination of a nugget and a spherical model did not fit November data satisfactorily as the semivariance was almost independent of distance, meaning that spatial dependence was random, i.e. a near-zero spatial autocorrelation length; thus the low standard deviations in November were therefore probably not representative of the true error due to the kriging method. The low spatial stability in April and November was likely explained by SST or biological activity (or both) being less spatially stable in these months (Jones et  al., 2012). Standard deviations of the kriging are included in our presented data files; a bias should not be introduced by the kriging itself (Pebesma, 1999).

A comparison of the different kriging approaches
The ordinary block kriging of the f CO 2 ,cl data was repeated using a range of sensible kriging parameters (Table 3). The standard deviation of the mean over the different kriging results was less than 5 µatm in most places, with higher values seen near the coasts, Arctic, and the western Tropical Pacific and Southern Ocean. These standard deviations were considerably smaller than those of the kriging itself (Figs. 7 and A4) but could be significant in a few places especially, but not exclusively, in the Arctic and coastal regions where the SOCAT data are particularly sparse.

Are some cruises more important than others?
The specific timing and track of a cruise may give an unrepresentative sample of that region and season. Therefore, it is important to investigate whether or not the final results are highly dependent on individual cruises. That possibility was studied using the bootstrap method, a statistical technique which permits the assessment of variability in an estimate using just the available data (Wilmott et al., 1985). Bootstrapping creates synthetic sets of data by random resampling from the original data with replacement. We bootstrapped the SOCAT data 10 times by cruise to estimate the variability of the mean monthly f CO 2 ,cl distributions. Due to the size of the data set we applied the bootstrapping in two stages, first by the cruise's unique identifier (cruise ID) for each year and region, and then by year and region. Each of the 10 resulting synthetic f CO 2 ,cl data sets were kriged as described in Sect. 4 (for each month in each synthetic data set the optimal variogram model was fitted and applied). The mean monthly distributions showed that in regions of fewer cruises (i.e. all regions except the North Atlantic and North Pacific) significant variation in f CO 2 ,cl could occur; the resulting variations can have a SD of up to 50 µatm. We con- clude that the final results are highly sensitive to individual cruises in many regions and additional caution in the results should be considered. High variability in the eastern-central equatorial Pacific could be a consequence of not excluding the El Niño years.

Temporal extrapolation error
The 1.5 µatm yr −1 rate of change in p CO 2 has an estimated precision of ±0.3 µatm yr −1 (Takahashi et al., 2009) and the trend for f CO 2 ,cl should follow the trend for p CO 2 ,cl (Eq. 6).
The error in f CO 2 ,cl (before the kriging step 6 in Sect. 3) due to uncertainty of the p CO 2 ,cl trend was therefore estimated for each sample station as ±(2010-year) × 0.3 µatm yr −1 and binned by month and in 1 • × 1 • grid boxes ranged between ±(0.9-5.7) µatm. The error was lowest in the North Atlantic Ocean and in the Pacific Ocean because more cruises were performed there in recent times. The absolute monthly mean extrapolation error over all grid points was estimated at 3.0 ± 0.1 µatm (average over all monthly means ± standard deviation). This implies that if in reality the rate of change since 1991 was 1.8 instead of 1.5 µatm yr −1 , our f CO 2 ,cl would be underestimated by ∼ 3 µatm on average. Recent research has shown that an error of this magnitude, or perhaps greater, is probable, since Takahashi et al. (2014) present an updated oceanic p CO 2 trend of 1.9 µatm yr −1 observed during the 20-year period 1993-2012, a value supported by McKinley et al. (2011).

Inversion error
Our conversion of f CO 2 ,is to p CO 2 (T eq ) could introduce an error if the data was not based on x CO 2 analysis (cruise flags not A or B), but on f CO 2 calculated from a spectrophotometer (very few cruises; Bakker et al., 2014), or if the investigator only provided f CO 2 ,is or p CO 2 ,is and did not use Eq. (A1) to correct for the temperature difference. This error was assessed by calculating the conversion from f CO 2 ,is to f CO 2 ,ym,i (Eq. 6) using SST and P eq instead of T ym and P eq, ym (expressed as f CO 2 ,ym,i=is ). This conversion would ideally produce the original SOCAT f CO 2 ,is value. A difference betweenf CO 2 ,is and f CO 2 ,ym,i=is implied that our recomputation differed from the one applied by SOCAT or the investigator and we called this difference averaged over one grid box "inversion error". Note that the error was the same for the measurement year as for the year 2010. This resultant calculated error was a small positive bias between 0 and 4 µatm; mostly near zero in the North Atlantic and several other areas, but with some higher levels in the Southern Ocean. The monthly mean inversion bias over all grid points was 1.0 ± 0.2 µatm (average over all monthly means ± standard deviation).

Absent values in our full f CO 2 re-computation
A problem related to the inversion error was introduced by absent data in our full f CO 2 re-computation (Sect. 3.3). By absent values we mean instances where in situ f CO 2 exist in the SOCAT data, but the related instantaneous variables were not measured, or not reported. The impact of these absent values did not always propagate into an inversion error because we made an effort to handle these absent values following SOCAT (Pfeil et al., 2014). For instance, if the in situ salinity or pressure data were not submitted to SOCAT, SOCAT used values from the respectively the World Ocean Atlas 2005 and NCEP for their conversion method. We note that absent values of temperature and pressure at the equilibrator could introduce systematic errors. Over all months and all years the percentages of these absent values were salinity 14 %, T eq 17 %, P 37 %, and P eq 41 %. The f CO 2 ,ym,i calculations were most sensitive to temperature. If T eq was not provided, we used in situ SST. In that case, the inversion error would be near zero but could lead to significant systematic f CO 2 ,ym,i errors. We therefore also reproduced our f CO 2 ,cl distribution maps using only data points with valid T eq values (not shown). These maps appeared to reveal fewer high f CO 2 ,cl outliers. If only data with valid T eq were selected the data quality was believed to be better, but the number of data points was compromised. Standard deviations calculated with the reduced data set were higher or lower than the standard values, depending on location and month. The monthly mean difference f CO 2 ,cl (all)f CO 2 ,cl (valid T eq ) ranged between −3.3 µatm (November) and 3.7 µatm (January) and was −0.4 µatm on average over all months. This result illustrates again that both the data sparsity and occasional missing equilibrator temperature data significantly affect the quality of our final f CO 2 climatology.

Measurement errors
Errors in the SOCAT measurements (f CO 2 ,is , T eq , P eq and SST) naturally propagated into f CO 2 ,cl uncertainty. The total of n independent errors ± x 1 , ± x 2 , . . .± x n is estimated by (x 1 ) 2 + (x 2 ) 2 + . . . + (x n ) 2 . The accuracies for the SO-CAT measurements that comply with the Standard Operating Procedures, SOP, criteria (Dickson et al., 2007;Pierrot et al., 2009) are given by Pfeil et al. (2013); these accuracies were the highest that could be expected as not all SOCAT data are of this high standard. Data sets with flags of C and D (59 % in version 1; Bakker et al., 2014) do not meet SOP criteria.
(In case of a flag of D the data may meet SOP criteria, but the metadata are incomplete). Likewise, the uncertainty in T ym,i had to be taken into account. Our NetCDF data give the SD values and counts (number of sea surface temperature pixels) with the mean SST skin values from ARC on a 1 • × 1 • grid. The average standard error, (SD/ months) was ±0.17 K. The uncertainty in the SST difference with subskin SST is ±0.1 K (Donlon et al., 1999). The total uncertainty in T ym, i was therefore estimated to be ±0.2 K (( 0.17 2 + 0.1 2 )). We estimated the propagation of these errors by applying the error for each parameter, x, and recalculating f CO 2 ,cl . (We calculated f CO 2 ,cl for the upper limit, x + x, and lower limit, x-x, and calculated the mean of the half of the resulting f CO 2 ,cl difference, f CO 2 ,cl = mean{(f CO 2 ,cl (x + x) − f CO 2 ,cl (x − x))/2}. The results are listed in Table 4. The total error caused by known uncertainties in the parameters was estimated to be > 3.7 µatm ( 0.75 2 + 0.015 2 + 2 2 + 3 2 ).

Summary of errors
The standard deviations produced by the kriging method (Sect. 5.2) are a function of both spatial variation of the data points and random errors in the f CO 2 ,cl values. The errors caused by the uncertainty of the rate of p CO 2 change (temporal extrapolation error) and measurement errors are such random f CO 2 ,cl errors but the magnitude of their propagation in the kriging procedure is difficult to calculate. Their monthly averages were estimated at ±3.0 µatm (Sect. 5.5) and ±3.7 µatm (Sect. 5.8) respectively and their total 4.8 µatm ( 3.0 2 + 3.7 2 ). Note that an error of 4.8 µatm is smaller than the average monthly minimum SD of the prediction of 6.3 ± 2.6 µatm (Sect. 5.2). The above analysis shows that the SD of the prediction (termed error) was dominated by the spatial variation of the data, an issue that is closely linked to data density (or sparsity). If we use the standard deviation of the kriging as an estimate of the prediction error, the prediction error of f CO 2 ,cl in a single grid cell ranged between ∼ 6 and ∼ 50 µatm and was ∼ 20 µatm average.
We estimated a bias of ∼ 1 µatm, introduced by the inversion step in the f CO 2 ,is to f CO 2 ,ym,i conversion (Sect. 5.6). The mean f CO 2 ,cl over all months had a bias of −0.4 µatm due to absent SOCAT values (Salinity, T eq , P and P eq ) in the re-computation (Sect. 5.7), so for the total bias of an annual average f CO 2 ,cl we estimate a value of ∼ 0.6 µatm. This is  .
less than the systematic bias in the global mean mean surface water p CO 2 of about 1.3 µatm as estimated by Takahashi et al. (2009) due to under sampling and their interpolation. The total bias in f CO 2 ,cl was dominated by the propagation of the uncertainty in the p CO 2 ,cl trend of ±3 µatm. Notice that the errors could be larger or smaller for individual months or regions. The difference between f CO 2 ,ym,i and f CO 2 ,is averaged over all years and grid boxes is relatively small (−1.21 µatm) compared to the uncertainty and biases in thef CO 2 ,cl estimations, and the consequence of our f CO 2 correction may not be large for calculation of the global mean climatological value of f CO 2 . However, the standard deviation of the mean difference, ±9.36 µatm, is not small and there are areas and periods where the bias is significant, especially when the sample density is high. The analysis of SST differences in Sect. 1.4 suggests that the original in situ temperatures, and therefore in situ f CO 2 values, are biased and that bias strongly varies spatially and seasonally. For regional and seasonal studies our conversion could therefore be much more relevant. In summary, it is clear that prediction errors are generally dominated by the effects of sparse sampling for most regions and seasons. Note that value of standard deviation in Fig. A4 varies from 5 to 57 µatm. Some of the prediction errors exceed 25 µatm and it is doubtful if the product is useful in those regions and seasons. Note that while other methods do not have such large explicit errors, it is possible that their true error is similar or greater, but that the error is obscured by a false assumption. Our method has the advantage that the problem with sparse sampling is explicit. The only reliable solution is better sampling and it is worth noting that the inclusion of new data in SOCAT v2 yields definite improvements (see next section). The most significant of the other sources of random errors are apparent from Table 4. The propagation of errors within the computation of f CO 2 ,cl prior to temporal extrapolation and kriging, is described in Sect. 5.8 and based on measurement errors estimated in Table 4. Note that the errors in f CO 2 ,is and T ym,i are the most significant. The total random error in each calculation of f CO 2 ,cl is estimated at > ∼ 3.7 µatm in Sect. 5.8. That error will contribute significantly to the prediction error in some of the better sampled regions. The systematic bias in measurements is relatively low and will result in only a small systematic global bias in f CO 2 ,cl (< ∼ 1 µatm). However, the assumed oceanic p CO 2 trend may be a greater source of systematic bias (perhaps 3 µatm), but that bias is difficult to put a firm value on without further study.

SOCAT version 2
The addition of new data points and the omission of bad and questionable data (Bakker et al., 2014) gave smoother global distributions and smaller prediction errors (Figs. 11 and A4-A6). The monthly average of the SD of the prediction was 17 ± 3 µatm (in comparison to 20 ± 5 µatm for version 1.5). A few specific regions show a definite improvement. For example, the prediction errors for the southwestern Pacific in DJF and MAM are greatly reduced between Figs. A4 and A6. The monthly mean difference f CO 2 ,cl (v1.5)f CO 2 ,cl (v2) ranged between −1.1 µatm (January) and 2.4 µatm (July) and was 0.3 µatm on average. Our climatology based on SOCAT version 2 data, reprocessed in a similar manner as the SO-CAT version 1.5 data, has also been made available with this paper.

Conclusions
We have combined SOCAT in situ data sets with a climatequality SST data set (ARC) to produce consistent sets of SST and CO 2 parameters suitable for climate change research of air-sea gas exchange. The f CO 2 (and p CO 2 ) predictions and standard deviations are computed for the year 2010 and interpolated to a global 1 • × 1 • grid, and have been made available together with other climatological data necessary to calculate global oceanic CO 2 fluxes. Two climatology data sets are presented as an online supplement to this paper, each consisting of 12 monthly NetCDF files: one using all SOCAT v1.5 data and one using all data of the recent update SOCAT v2. We identified and calculated various possible errors. The random errors due to the spatial interpolation, closely related to data density, dominated, but all errors vary spatially. The data quality/density in the North Atlantic and North Pacific proved to be superior, and thus these regions have the lowest prediction errors (∼ 6 µatm in the best sampled areas). The products have been verified by checking that key and established features such as the seasonal amplitude in the North Atlantic and North Pacific are similar to those reported in other studies. Other regions show much larger prediction errors (often exceeding 25 µatm), highlighting the issue of insufficient sampling. Other interpolation methods may yield nominally lower prediction errors, but that may only obscure the issue of sparse sampling. If we use the standard deviation of the kriging to calculate the prediction error, the prediction error of f CO 2 ,cl in a single grid cell ranged between ∼ 6 and ∼ 50 µatm and was ∼ 20 µatm on average.
Our products are referenced to a particular year (2010), but can be corrected to a reasonable estimate for another year by reapplying the assumed trend in oceanic p CO 2 (1.5 µatm yr −1 ). The necessity of using multi-year in situ oceanic CO 2 data to supply adequate data for global calculations is invidious; it would be preferable to make genuine single-year calculations. The bias uncertainty in f CO 2 ,cl was dominated by the assumed value of the oceanic p CO 2 trend, which might introduce a systematic global bias of about ±3 µatm into the 2010 products.
Our data set based on SOCAT version 2 is very similar to that derived from SOCAT version 1.5. However, we recommend that users exploit the version that is based on SO-CAT version 2, as it is derived from a larger in situ data set and higher quality data. SOCAT asks all data providers to include T eq in their data submission. The absence of equilibrator temperatures from some data sets submitted to SOCAT is unfortunate. It would benefit climatological applications if the equilibrator temperature and f CO 2 at the equilibrator temperature was always included in future versions of SO-CAT, negating the need for the inversion step described in this paper. Conversion between the temperature of sea water in the equilibrator and a monthly composite temperature from a global, long-term, homogenous, highly stable SST data set such as ARC (Eqs. 5 and 6) could also be included as an additional parameter to provide another standard product in parallel with the direct in situ products.  Table A1. Definitions of the different parameters used in the calculations throughout this paper.

Name
Unit Meaning p CO 2 µatm Partial pressure of CO 2 in seawater f CO 2 µatm p CO 2 adjusted to account for the fact that the gas is not ideal regarding molecular interactions between the gas and the air x CO 2 ,dry ppm Mole fraction of CO 2 in dry air x CO 2 ,wet ppm Mole fraction of CO 2 in wet air (100 % humidity) S Salinity SST • C or K Sea surface temperature in general, and in situ measurement of water temperature at depth by SOCAT if not stated otherwise. SST skin K SST at the sea surface skin (Fig. 1). In this paper represented by monthly 1 • × 1 • grid-box average of SST skin derived from the ARC data set (Merchant et al., 2012) without differentiating between day-and night-time measurements. SST MBL • C or K SST at the bottom of the mass boundary layer (Fig. 1) SST subskin K SST at the bottom of the thermal skin (Fig. 1); in this paper estimated by SST skin + 0.14 SST depth • C or K a SST in metres below the surface (Fig. 1). In this paper represented by SOCAT's in situ measurement. SST 5 m • C or K a SST at 5 m water depth T ym K Monthly 1 • × 1 • grid box mean of SST subskin dT K dT = T ym -corresponding grid box mean of SOCAT's instantaneous in situ SST measurements T eq • C or K Temperature in the equilibrator chamber P eq atm b Pressure in the equilibrator chamber P w atm b Water vapour pressure at T eq P atm atm b Atmospheric pressure a In SOCAT regional synthesis files: • C. b In SOCAT regional synthesis files: hPa. The Supplement related to this article is available online at doi:10.5194/os-11-519-2015-supplement.