From January 2011 to January 2014, a FerryBox system was installed on the Voluntary Observing Ship (VOS) Armorique (Brittany Ferries). This vessel crossed the English Channel between Roscoff (France, 48∘43′38 N, 3∘59′03 E) and Plymouth (United Kingdom, 50∘22′12 N, 4∘08′31 E; Fig. 1) up to three times a day. The FerryBox continuously measured sea surface temperature (SST), salinity and partial pressure of CO2 (pCO2, from April 2012) along the ferry track with more than 600 crossings with pCO2 acquisition. Between January 2011 and January 2014, discrete sampling was performed on 57 return crossings between Roscoff and Plymouth with a total of 1026 sampling locations in the WEC. During each cruise, 18 water samples were taken from the FerryBox seawater circuit for the determination of dissolved inorganic carbon (DIC), total alkalinity (TA) and associated salinity and nutrient concentrations (Marrec et al, 2013). Seawater pCO2 values were calculated from TA, DIC, temperature, salinity and nutrient concentrations with the CO2SYS program (Pierrot et al., 2006) using the equilibrium constants of CO2 proposed by Mehrbach et al. (1973), refitted by Dickson and Millero (1987) on the seawater pH scale, as recommended by Dickson et al. (2007). The methods used for the analytical determinations of DIC and TA are described in detail in Marrec et al. (2014) and gave accuracies of ±2 and 3 µmol kg-1, respectively. Thus, the computed values of pCO2 from DIC and TA have uncertainties at the lower end of ±6 µatm (Zeebe and Wolf-Galdrow, 2001). Sensors were calibrated and/or adjusted based on these bimonthly discrete measurements as described in Marrec et al. (2014). Based on the comparison between high-frequency pCO2 data obtained with a Contros HydroC/CO2 FT sensor and bimonthly pCO2 data calculated from DIC/TA, we estimated high-frequency pCO2 measurements uncertainties at the lower end ±6 µatm (Marrec et al., 2014), in the same range as computed values of pCO2 from DIC and TA. We built a composite monthly data set of in situ SST and pCO2 data over 3 years based on both high-frequency and bimonthly (twice a month) measurements. We used bimonthly discrete pCO2 data between January 2011 and April 2012 and high-frequency pCO2 data from April 2012 to January 2014. The monthly pCO2 data were then adjusted to reference month July 2012, for MLR computation, using an atmospheric growth rate of 0.15 µatm month-1 (1.8 µatm yr-1) and assuming that the surface ocean pCO2 is growing at the same rate as the atmosphere. This growth rate was calculated from atmospheric pCO2 at Mace Head (Ireland, see Sect. 3.5 for further details) from January 2003 to December 2013 and is then representative of our study area.

Satellite-derived Chl a concentrations (µg L-1) were acquired from the Moderate Resolution Imaging Spectroradiometer (MODIS) aboard the Aqua satellite. Daily images were provided by the Natural Environment Research Council (NERC) Earth Observation Data Acquisition and Analysis Service (NEODAAS) at a spatial resolution of 1.1 km. Monthly mean Chl a estimates were computed from January 2003 to December 2013 from these individual images over our study area (Fig. 1). WEC, CS and IS waters are optically complex shelf waters (Joint and Groom, 2000; Darecki et al., 2003; McKee et al., 2007). These shelf seas present both Case 1 and Case 2 optical water types (Morel and Prieur, 1977; Morel et al., 2006) depending on their hydrographical properties (seasonally stratified or homogeneous), the proximity to the coast, and the period of the year. In Case 1 waters, the optical properties are dominated by chlorophyll and associated degradation products as in open ocean waters. In coastal waters, classified as Case 2, suspended particulate sediments and yellow substances of terrestrial origin induce important biases on chlorophyll a concentration estimates and special algorithms have been developed for these waters (Gohin et al., 2002). As shown by Groom et al. (2009), who explain how a coastal station in the nWEC (L4) can be considered as Case 1 or Case 2 depending on various parameters, it is difficult to label our studied provinces as Case 1 or Case 2 waters. However sWEC, LE and IS present more similarities with Case 2 waters, especially during winter, whereas nWEC and CS are closer to Case 1 waters. The NEODAAS provided satellite Chl a estimates based on the OC3 algorithm, more specific to Case 1 waters, and on the OC5 algorithm (Gohin et al., 2002), developed in coastal waters of the eastern English Channel and the Bay of Biscay affected riverine input (Seine, Loire, Gironde). Chl a estimates based on the OC3 algorithm show enhanced Chl a concentrations during winter, particularly in near-coast and in well-mixed provinces, whereas Chl a estimates from the OC5 algorithm tend to underestimate the Chl a concentrations especially during spring and summer (data not shown). We chose to use the OC3 algorithm in this study, which seemed more suitable and more representative of the biological activity dynamics, and we gridded monthly 1.1 km satellite data into 0.05∘ × 0.05∘ grid cells over our study area. We extracted monthly mean Chl a values along the ship track from January 2011 to December 2013 (Fig. 3b) to predict pCO2 based on MLRs (see below).

Satellite-based SST (∘C) data were acquired from the Advanced Very High Resolution Radiometer (AVHRR) instrument. Monthly mean SST estimates were computed from January 2003 to January 2014 from individual images with a spatial resolution of 1.1 km by the NEODAAS. A validation between monthly in situ SST and associated satellite SST showed a robust correlation (R2= 0.97, N= 448, p < 0.001 and RMSE = 0.43 ∘C). We gridded 1.1 km resolution satellite SST into 0.05∘ × 0.05∘ cells as with all other remotely sensed and modeled parameters.

Photosynthetically active radiation (PAR, in E m-2 d-1) data were retrieved from the Ocean Biology Processing Group (McClain, 2009; http://oceancolor.gsfc.nasa.gov). We used the Level 3 monthly merged PAR product from MODIS Aqua. PAR was used as a variable in the MLRs as an indicator of the amount of light available for phytoplankton, which presented inter-annual variation over our study period (Fig. 3c). Based on the observations of L'Helguen et al. (1996), Marrec et al. (2014) suggested that light availability might be an important factor responsible for the strong inter-annual variability of phytoplankton blooms in the sWEC.

Mixed layer depth (MLD), which was one of the variables used in algorithm development for the seasonally stratified nWEC and in the spatial extrapolation of this algorithm in the adjacent CS, was computed from the MARS3D model (Lazure and Dumas, 2008; Berger et al., 2014) developed in the PREVIMER project (Charria and Repecaud, 2014). MLD was defined as the shallowest depth corresponding to a temperature or density difference with the surface water higher than δT= 0.5 ∘C or δDens = 0.125 (Monterey and Levitus, 1997). We compared the model outputs with MLD calculated from the temperature and salinity profile at the fixed station E1 off Plymouth (50.03∘ N, 4.37∘ W; depth 75 m) from January 2006 to January 2014 (Fig. S1 in the Supplement). Measurements were undertaken every 2 weeks by the Western Channel Observatory (NERC National Capability of the Plymouth Marine Laboratory and Marine Biological Association, www.westernchannelobservatory.org.uk). Profiles were obtained by a Seabird SBE 19+ with precision for temperature and computed salinity of 0.005 ∘C and 0.002, respectively. We also compared the modeled MLD in the CS and at the E1 fixed station with Armor-3D L4 Analysis observation products provided by the Copernicus Marine Environment Monitoring Service (ex-MyOcean, http://marine.copernicus.eu). The latter are combined products from satellite observations (sea level anomalies, mean dynamic topography and sea surface temperature) and in situ (temperature and salinity profiles) data on a 1/2∘ regular grid in our study area. Modeled and in situ (from the Western Channel Observatory) MLD at the E1 station showed a robust correlation (R2= 0.82, N= 89, Fig. S1). Comparing modeled and Armor-3D L4 Analysis observation products MLD of CS (Fig. S1) clearly showed the robust approximation of MLD by the model, particularly concerning the start and the end of stratification, despite a small overestimation of the modeled MLD. These comparisons validated the use of modeled MLD in our computations. Modeled MLDs were gridded in the 0.05∘ × 0.05∘ grid in seasonally stratified provinces and were extracted along the ship track in the nWEC to be included in the pCO2 algorithms. We chose to use the MLD over depth ratio (MLDr) in the MLR computation instead of MLD. During winter in seasonally stratified areas, the whole water column is mixed. However, depths are not homogeneous (ranging from -20 to -200 m); thus the use of MLD winter values, which corresponded approximately to the bathymetry, would lead to bias in MLR computation. MLD, in our algorithms, was only an indicator of the presence or absence of stratification of the water column, particularly concerning the start and the end of stratification. Figure 3e shows the monthly MLDr ratio in the nWEC between Roscoff and Plymouth.

Monthly wind speed data (WND, in m s-1) corrected to 10 m height were obtained from four-times-daily wind speed products from the ERA-interim re-analysis project (Dee et al., 2011) produced by the European Centre for Medium-Range Weather Forecasts (ECMWF). We extracted the 0.125∘ latitude by 0.125∘ longitude global grid wind speed values over the study area, and we gridded these data into our 0.05∘ × 0.05∘ grid. We used WND data in the computation of the gas transfer velocity of CO2 (k) as an indicator of wind stress for the calculation of air–sea CO2 fluxes (Sect. 3.5). Figure 3d shows the monthly WND values used in the algorithm development along the ferry route from 2011 to 2013.

We developed two specific algorithms to estimate surface seawater pCO2 in each of the hydrographical provinces of the WEC (seasonally stratified nWEC and permanently well-mixed sWEC) in order to apply them on a larger spatial and temporal scale in the adjacent Celtic and Irish seas. We used MLRs to predict pCO2 in each province based on monthly mean values of Chl a, SST, PAR, WND (for the sWEC), MLD (for the nWEC) and from a time variable TI (Eqs. 1 and 2) representative of the seasonality (Friedrich and Oschlies, 2009; Lefèvre et al., 2005; Signorini et al., 2013) according to pCO2, MLR=a0+∑i=1nai⋅piTI=sin⁡2⋅π⋅(Day-α)365, where pCO2, MLR is the predicted pCO2, a0 is the intercept of the MLR and ai is the coefficient related to each variable pi. In Eq. (2), “Day” is the 15th day of each month (Julian day) and α a value between 0 and 365 chosen by iteration to optimize the seasonal phasing until the minimum standard deviation on residuals and the best correlation coefficient R2 are obtained by the MLR. All of these parameters were gridded in 0.05∘ latitude intervals (Fig. 3 and 5) between 48.80∘ N (off Roscoff) and 50.20∘ N (off Plymouth). The northern latitude limit of 50.20∘ N is relatively far from Plymouth in order to exclude effects of freshwater inputs from the Tamar and Plym rivers, which influence the biogeochemical properties of the area (Smyth et al., 2009) and are not representative of nWEC waters. The WEC is divided into sWEC and nWEC at 49.40∘ N from the average position of the thermal front separating the two hydrographical provinces during the period of study (Fig. 2 and Marrec et al. 2014). MLRs were applied on these gridded monthly values in each province using the “regress” Matlab^® function. The performance of regional algorithms was evaluated by the correlation coefficient R2, the adjusted R2, the root-mean-square error (RMSE) and the p values (for each of the parameters and for the regression). These parameters represent the capacity (the R2 and the adjusted R2 ) and uncertainty (RMSE) of the algorithms to predict pCO2. The coefficient of determination R2 indicates the amount of total variability explained by the regression mode. The adjusted R2 is the coefficient of determination of the MLR adjusted to the degree of freedom, which depends on the number of variables used. In each MLR presented in the study, the adjusted R2 and R2 were similar; thus only R2 is presented.

MLR coefficients were calculated based on our 3-year data set, and the goal of the study is to apply the algorithms over a decade (2003–2013) over the study area (Fig. 1). Based on the atmospheric pCO2 calculated from Mace Head atmospheric xCO2, we calculated a regional anthropogenic increase in atmospheric CO2 of 1.8 µatm yr-1, a similar rate as mentioned by Thomas et al. (2008) and Le Quéré et al. (2010). We assumed that the ocean surface pCO2 increase is trending at the same pace as the atmospheric pCO2. Thus we consider a regional increase of seawater pCO2 of 1.8 µatm yr-1 representative of our study region. When we computed the algorithms, we considered this factor in the computations by adding a correction term ΔX (Eq. 3) on the right term of Eq. (1) (Shadwick et al., 2010; Signorini et al., 2013) with ΔX=1.812⋅Δm, where Δm (month) is equal to the number of months since July 2012, the middle of our study period (2011–2013). For example, in January 2013, ΔX would be equal to (1.8/12)×(+6) and in January 2012 ΔX would be (1.8/12)×(-6). The same reference month (i.e., July 2012) was used to extrapolate the algorithms from January 2003.

We normalized each of the variables pi (Eq. 4) using the mean (pi,m) and standard deviation (pi,SD) of pi over the study period. The normalized coefficients, which are directly comparable and dimensionless, allowed us to evaluate the relative contribution, or weight, of each of the independent variables (i.e., SST, Chl a, TI, wind speed, PAR and MLD) in the prediction of the dependent variable (i.e., pCO2, MLR). pi,s=(pi-pi,m)pi,SD

The Surface Ocean CO2 ATlas (SOCAT) database (http://www.socat.info/; Bakker et al., 2014) is an international collection of underway ocean CO2 measurements. This compilation currently includes approximately 10.1 million measurements from more than 2660 data sets from 1968 to 2011. The Lamont–Doherty Earth Observatory (LDEO) pCO2 database Version 2013 (Takahashi et al., 2014) lists ∼ 9 million surface ocean pCO2 measurements made since 1957. From January 2003 to January 2011, 64 800 pCO2 and associated SST/SSS values were available over the study area (Fig. 4, Table 1). From 2003 to 2014, in sWEC, nWEC and sCS, pCO2 values from SOCAT were available for 50 to 65 % of the months (Table 1), mainly from the same southwest–northeast route (Fig. 4) operated principally by three voluntary observing ships (Lüger et al., 2004; Steinhoff, 2010; Schuster et al., 2013; Lefèvre et al., 2014; more details available on the SOCAT website) which crossed these provinces up to twice per month, almost every month from 2003 to 2011. In nCS and IS, the data coverage was sparser and in LE very few data were available. We binned all of these data into the study grid on a monthly basis. We binned the SOCAT and LDEO data into 0.05∘ × 0.05∘ grid and computed the mean monthly value in each grid cell. The performance of the model was obtained by comparing the mean observed and predicted monthly value per grid cell (see Fig. S2 and 2). For each province, the observed and predicted monthly mean based on this 0.05∘ × 0.05∘ grid in each province are plotted in Fig. 8.

The fluxes of CO2 across the air–sea interface (F) were computed from the pCO2 air–sea gradient (ΔpCO2=pCO2  water- pCO2  air, µatm) according to F=k⋅K0⋅ΔpCO2, where k is the gas transfer velocity (m s-1) and K0 is the solubility coefficient of CO2 (mol atm-1 m-3) calculated after Weiss (1970). The exchange coefficient k (Eq. 6) was computed as a function of wind speed with the algorithm given by Nightingale et al. (2000) established in the southern bight of the North Sea (SBNS). The SBNS and the WEC present similar environmental characteristics: these two shallow continental shelves are both close to land with high tidal currents controlling the physical structure of the water column. k=0.222⋅C2⋅u102+0.333⋅u10⋅Sc660-0.5, where u10 is the wind speed data at 10 m height (m s-1), Sc the Schmidt number at in situ SST and C2 the nonlinearity coefficients for quadratic terms of the gas transfer relationships according to Wanninkhof et al. (2002): C2=1n∑j=1nuj2/umean2, where uj is the high-frequency wind speed (m s-1), umean is the monthly mean wind speed (m s-1) and n the number of available wind speed data in the month. The empirical relationships of gas transfer with wind speed are nonlinear; then, by using monthly mean wind speeds, the temporal distribution of the wind speeds over the month will affect the gas transfer velocity. We apply the same method reported by Jiang et al. (2008) to account for the intrinsic variability of monthly wind speed data.

We also computed gas transfer velocity with the Wanninkhof (1992) and with the Wanninkhof and McGillis (1999) parameterizations for long-term winds to give a range of computed air–sea CO2 fluxes and we used the nonlinearity coefficients for quadratic and cubic terms of the gas transfer relationship (Wanninkhof et al., 2002; Jiang et al., 2008). Wind speeds along the ferry track and over the study area were extracted from four-times-daily wind speed data corrected at 10 m height from the ERA-interim re-analysis project (Sect. 3.2). Atmospheric pCO2 (pCO2  air) was calculated from the CO2 molar fraction (xCO2) at the Mace Head site (53∘33′ N, 9∘00′ W; southern Ireland) of the RAMCES network (Observatory Network for Greenhouse gases) and from the water vapor pressure (pH2O) using the Weiss and Price (1980) equation. Atmospheric pressure (Patm) over the study area was obtained from the ERA-interim re-analysis project (Dee et al., 2011).

To estimate the uncertainties of the monthly air–sea CO2 flux values, we follow the error propagation method exposed in Omar et al. (2007) and used in Lauvset et al. (2013). Uncertainties were expressed by the random error associated with the monthly flux values (σF) according to σF=∂F∂K0×σK02+∂F∂k×σk2.+∂F∂ΔpCO2×σΔpCO22+2∂F∂K0∂F∂kCovK0k+2∂F∂K0∂F∂ΔpCO2CovK0ΔpCO2+2∂F∂k∂F∂ΔpCO2CovkΔpCO21/2, where σK0, σk and σΔpCO2 are the uncertainties associated with K0, k and ΔpCO2, and Covxy denotes the covariance between any two parameters x and y. The total uncertainty in k is based on an assumed 1 m s-1 uncertainty in the wind speed data and from the 0.43 ∘C uncertainty of the AVHRR satellite-based SST (Sect. 3.2), which impact the Schmidt number calculation and ranged between ±13 and ±41 m month-1. The uncertainty in K0 is obtained by summing a 0.5 % uncertainty in the computation of K0 (McGillis and Wanninkhof, 2006) and the 0.43 ∘C error in the AVHRR satellite-based SST, which corresponds to a 1.4 % uncertainty. The uncertainty in K0 ranged between ±0.66 and ±0.94 mol C m-3 atm-1. The total uncertainty in ΔpCO2 results from the quadratic sum of the total uncertainty in pCO2,  MLR (15.9 µatm in permanently well-mixed provinces and 17.1 µatm in seasonally stratified provinces; Sect. 4.1) and an assumed ±1 µatm uncertainty in the atmospheric pCO2. The covariances were obtained by holding all parameters at their mean values, except SST, and by using the changes in K0, k and ΔpCO2 due to SST to determine these covariances. Depending on the provinces, CovK0k varied between -12.96 and -27.61, CovK0ΔpCO2 between 3.15 × 10-5 and 1.05 × 10-4 and CovkΔpCO2 between -3.94 × 10-4 and -1.05 × 10-4. For further details on the calculation of the terms used in Eq. (7) see Omar et al. (2007). The random error associated with the mean annual flux estimates was calculated as the quadric sum of the uncertainties in the monthly mean fluxes. Thus, air–sea CO2 fluxes in the paper and figures are given with their computed uncertainties.

We performed MLRs to estimate surface pCO2 based on SST, Chl a, the time variable TI, WND and PAR in the sWEC, and by including MLDr (MLD / depth ratio) and without WND in the nWEC. Table 2 shows the MLR-normalized coefficients used in the algorithms and their evolutions when we added new variables in the computations. The corresponding R2 and RMSE are the indicators of the performance of the MLR at each addition of a new variable. Based on SST, Chl a, PAR, 398 and 510 monthly gridded observations, we obtained R2 of 0.61 and 0.69 with RMSEs of 22.2 and 22.6 µatm, in the sWEC and nWEC respectively (Table 2). The inclusion of WND in sWEC and MLDr in nWEC increased R2 values up to 0.62 and 0.73 with respective RMSE of 22.2 and 21.0 µatm. The inclusion of the time variable TI considerably improved the performance of the MLR, with R2 values of 0.80 and 0.82 and RMSEs of 15.9 and 17.1 µatm, in sWEC and nWEC, respectively (Table 2, Fig. 6a and b). It is worth noting that when excluding Chl a in the MLR, R2 decreased by 0.03 and 0.05 and RMSE increased by 1.4 and 2.1 µatm in sWEC and nWEC, respectively. Overall, the RMSE accounted for less than 10 % of the amplitude of the pCO2 signal (approximately 200 µatm). For each variable and each MLR, we calculated the p values, which were all smaller than 0.001 (not shown in Table 2), meaning that all of the variables were statistically significant in the MLR.

From the normalized coefficients, we calculated the percentages of variability explained by each variable. The seasonal pCO2 signal followed an average dynamic close to a sinusoidal signal, with maximal values in fall and minimal values in spring, with transitional values in winter and summer. Therefore, the time variable TI, which is a sinusoidal function, contributed to more than half of the variability of the pCO2 signal, highlighting the strong seasonality observed on this signal (Fig. 5a, Table 2). Beside TI, the most significant variables in terms of relative contribution were SST and PAR, with 22 and 15 % in sWEC and both with 15 % in nWEC, respectively. Chl a contributed 7 and 6 % in the sWEC and nWEC, respectively, a relatively low value considering that, as reported by Marrec et al. (2013), biological processes are the main driver of seasonal pCO2 variability in the WEC. The addition of MLDr improved the performance of the MLR despite its relatively small contribution compared to the other normalized coefficients. Due to the complexity of the algorithms, a quantitative interpretation of non-normalized coefficients is difficult. For example, according to our model, pCO2 decreases by 14.4 µatm when SST increases by 1 ∘C (Table 2). This value contradicts the expected thermodynamic relationship between SST and pCO2 from Takahashi et al. (1993). The goal of this study was to develop suitable algorithms to predict pCO2 variability in continental shelf seas by maximizing the performance of the MLR and not to define empirical relationships between the variables and pCO2.

Figures 5a, b and c show the monthly gridded (0.05∘ of latitude) pCO2, pCO2 predicted from MLR coefficients (pCO2, MLR) and associated residuals (pCO2, obs – pCO2, MLR) from January 2011 to January 2014 between Roscoff and Plymouth. In the sWEC, pCO2 values lower than 350 µatm were observed during spring 2011, whereas in the same period in 2012 and 2013, pCO2 remained close to the atmospheric equilibrium, between 350 and 400 µatm. Thus, the dynamics of pCO2 in both provinces presented important inter-annual variability. As the pCO2 simulation by the MLR is mainly driven by a seasonal cycle (TI), which is the same every year, these inter-annual discrepancies can yield bias in the MLR simulation. For the sWEC the MLR model overestimated pCO2 during spring and summer 2011 (residuals up to 30 µatm, Fig. 5b and c) and underestimated pCO2 in spring 2012 (residuals down to -50 µatm, Fig. 5b and c) by simulating an average decrease of pCO2 both years. In Fig. 6c and d, residuals are plotted vs. observed pCO2 in the sWEC and nWEC, and in Fig. 6e and f monthly mean residuals over each province are plotted vs. months from January 2011 to December 2013. In the sWEC, when observed pCO2 (pCO2, Obs) values were below 350 µatm, as in spring 2011, pCO2, MLR values were much higher than pCO2, Obs and residuals were highly negative. In the sWEC, residuals as a function of the observed pCO2 were not homogeneously distributed, especially during year 2011 (Fig. 6), with high negative residuals when pCO2 was below 350 µatm and high positive residuals when pCO2 was over 450 µatm. In the nWEC, the distribution of residuals was more homogeneous (Fig. 6c and d); the less pronounced inter-annual variability was responsible for the better performance of the algorithms (R2) in this part of the WEC.

Shadwick et al. (2010) and Signorini et al. (2013) undertook similar studies on the Scotian shelf and the northeastern American continental shelf, respectively. They estimated pCO2 as a function of SST, Chl a and k, and from SST, salinity, Chl a and a time variable (TI), respectively, using MLR. Based on 14 monthly mean values from a high-frequency data set at a moored buoy, the algorithm developed by Shadwick et al. (2010) attained a R2 of 0.81 with an associated standard error of 13 µatm. They extrapolated this algorithm over the entire Scotian shelf region to investigate pCO2 and air–sea CO2 fluxes from remotely sensed data from 1999 to 2008. Signorini et al. (2013) reported R2 and associated RMSE ranging from 0.42 to 0.87 and from 22.4 to 36.9 µatm, respectively. They divided the northeastern American continental shelf into five distinct regions according to their physical and biogeochemical attributes. Their studies were based on SOCAT surface ocean pCO2, and the environmental variables used to predict pCO2 came from remotely sensed and modeled data. The performances of our MLRs are within the same range as those in these previous studies. We developed our algorithms based on a 3-year data set obtained during highly contrasting years, which contributed to the robustness of our model to predict a representative seasonal cycle of pCO2 as seen in the nWEC. However, the WEC is a highly dynamic continental shelf ecosystem characterized by strong inter-annual variations. Very exceptional events, inherent to continental shelf areas, remain difficult to simulate with our method, which explain the lower performances of our MLR for the sWEC, as seen from the high residuals observed during 2012.

We compared air–sea CO2 fluxes (Eq. 5) calculated from observed pCO2 and from pCO2 simulation (Fig. 7 and Table 3). Figure 7 shows the air–sea CO2 flux variation in the sWEC and the nWEC based on pCO2, obs and pCO2, MLR from January 2011 to January 2014. Fluxes were computed from the mean monthly pCO2 of each province, and the standard deviation on MLR fluxes corresponds to MLR fluxes computed plus and minus the RMSE obtained in the respective provinces (Table 2). Seasonal air–sea CO2 flux cycles were well described by the algorithm-defined pCO2, particularly for the nWEC, with both provinces acting as a sink of atmospheric CO2 during spring and summer and as source of CO2 to the atmosphere during fall and winter. The inter-annual variability of pCO2 observed in the sWEC during spring and summer was also reflected in the flux computations, the fluxes based on MLR overestimating the CO2 sink in spring 2012. Table 3 reports the annual flux estimates in both provinces based on in situ pCO2 observations and pCO2, MLR. On an annual scale, the seasonally stratified nWEC waters acted as a sink of atmospheric CO2 at a rate of 0.0 to 0.5 mol C m-2 yr-1 based on in situ pCO2 measurements. Fluxes computed from pCO2, MLR also indicated that the nWEC acts as a sink of atmospheric CO2, but we observed some discrepancies between the magnitude of in situ and MLR-based fluxes. The permanently well-mixed sWEC waters acted as a source of CO2 to the atmosphere from 2011 to 2013 ranging between 0.5 and 0.8 mol C m-2 yr-1, and annual CO2 fluxes computed from observed and modeled pCO2 were in good agreement. The performances of our algorithms to estimate monthly surface pCO2 allowed us to compute suitable air–sea CO2 fluxes in WEC provinces during three contrasted years.

We applied the previous algorithms (Sect. 4.1) over our study area (Fig. 2) from monthly mean remotely sensed and modeled parameters in the permanently well-mixed sWEC, IS and LE and in the seasonally stratified nWEC, sCS and nCS. The pCO2 values computed from these variables were averaged by province from January 2003 to December 2013 (Fig. 8). The available SOCAT and LDEO observed pCO2 data (Fig. 4 and Table 1) were binned into 0.05∘ × 0.05∘ grid cells and averaged over the provinces. Observed pCO2 monthly mean data were superimposed on the algorithm pCO2 time series (Fig. 8).

For the nWEC (Fig. 8d), the modeled data followed the main features of the seasonal cycle described by the observed data and were in relatively good quantitative agreement (see Fig. S2 for more details). Spring pCO2 minima were in the same range, despite the discrepancy of timescales. During fall and winter, maximum values were not always reached, suggesting a relatively small overestimation of modeled pCO2 values at this time. In the sCS (Fig. 8c), where observed data covered most months from 2003 to 2013, predicted data fitted reasonably well the observed pCO2 during spring and summer. During fall and winter, only few observed pCO2 data were above equilibrium values, but the model predicted surface water pCO2 oversaturation compared to atmospheric equilibrium. Despite the limited number of observed data available for the nCS, IS and LE, the model predictions were in good agreement with the observed pCO2 (Fig. 8 and S2). For the sWEC (Fig. 8e), the predicted pCO2 values were higher than the observed data, our algorithm thus mainly overestimating the pCO2. During spring, the minimal observed pCO2 values were not always reached by the model. Figure 4 shows that the observed pCO2 data available for the sWEC were acquired along the Ushant front (Pingree et al., 1975; Morin, 1984; Sournia et al., 1990) at the border of the province (sWEC, nWEC and sCS) delimited based on summer SST (Fig. 2). This border is a frontal zone between well-mixed and stratified systems with enhanced biological activity due to the constant supply of nutrients from the deep layer of stratified systems, especially in summer when the winter nutrient stock is totally depleted (Holligan, 1981; Morin, 1984, Le Fèvre, 1986, Le Boyer et al., 2009). This enhanced productivity might induce biological consumption of CO2, which would explain the overestimation of modeled pCO2 in the frontal zone. The SOCAT and LDEO data were not representative of a homogeneous system, hindering a direct comparison.

Directly comparing monthly mean pCO2 values obtained from algorithms and the SOCAT and LDEO pCO2 data could generate an important bias because of the timescale difference between these data sets. Monthly gridded SOCAT and LDEO data were mainly based on measurements performed at daily scales. Computed pCO2 values were representative of the average monthly pCO2 variability, which tends to smooth extreme values obtained at shorter timescales and prevent any observation of short-term processes. Despite this timescale discrepancy the mean differences between observed and predicted pCO2 were -1 ± 27 in the sCS, -3 ± 25 in the nWEC, 3 ± 26 in the nCS, -7 ± 26 in the IS and -3 ± 29 µatm in LE on an annual scale. Considering the uncertainties relative to the MLR of 17 µatm (Sect. 4.1), these results were very promising and allowed us to validate the extrapolation of our method over our study area. The results obtained in the sWEC, with an annual mean difference of -14 ± 26 µatm, were less promising as explained above and in Sect. 4.1. The comparison of SOCAT and LDEO data with the model predictions provided indications on the MLR performance on a wider spatial scale. For the first time, we thus computed the seasonal and long-term dynamics of pCO2 and associated air–sea CO2 fluxes over a decade for this part of the northwestern European continental shelf (Sect. 4.3) despite the relative uncertainties inherent to the method.