4.1. Carbon Dioxide System
 We used CT, AT, salinity, temperature and depth for each sample as input parameters in a CO2-chemical speciation model (CO2SYS program [Pierrot et al., 2006]) to calculate the carbon dioxide partial pressure of (pCO2), carbonate ion concentration ([CO32−]), and the saturation state (Ω = [CO32−] * [Ca2+]/K*sp) with respect to aragonite (ΩAr) and calcite (ΩCa). We used the CO2-system dissociation constants (K*1 and K*2) estimated by Roy et al. [1993, 1994], since an internal consistency study showed them to be the most suitable constants for cold and fresher surface waters [Chierici and Fransson, 2009]. Calculations using the Roy et al. [1993, 1994] constants yield slightly higher ΩAr and ΩCa values than those derived from other CO2-system constants, such asMehrbach et al.  (refit by Dickson and Millero ). The calculations were performed on the total hydrogen ion scale (pHT) using the HSO4- dissociation constant of Dickson . The calcium concentration, [Ca2+], was assumed to be proportional to salinity, 10.28xSp/35 μmol kg−1, where Sp is the practical salinity. The stoichiometric solubility constants for aragonite and calcite (K*sp) were taken from Mucci  and corrected for pressure according to Ingle . If Ω < 1, solutions are undersaturated, whereas, for Ω > 1, they are supersaturated with respect to the mineral of interest. The CO2SYS calculations were performed without the soluble reactive phosphate (SRP) and silicic acid (Si(OH)4) concentrations, introducing a mean error of approximately 0.8% in the [CO32−] and calcium carbonate saturation state estimates.
4.2. Water Mass Fractions
 The relationships between salinity and AT, were used to determine the end-member signatures of the two freshwater sources (meteoric water and sea ice meltwater) and the polar mixed layer (Table 1), according to well-established protocols [Macdonald et al., 1999, 2002; Cooper et al., 2008; Fransson et al., 2001, 2009]. The ATand salinity end-member values for sea ice meltwater were estimated from the AT and salinity measured in melted sea ice samples (ATice and Sice, respectively, N = 166) collected during the CFL project (Fransson et al., unpublished manuscript, 2011). The mean ATand salinity of the sea ice meltwater end-member (ATSIM and SSIM) were estimated to 509 ± 32 μmol kg−1 and 7.4 ± 0.5, respectively.
Table 1. Source Water Salinity and Total Alkalinity (AT) for River Runoff (Meteoric Water, MW), Sea Ice Meltwater (SIM), and the Polar Mixed Layer (PML)
|Source Water||S||AT (μmol kg−1)||References|
|MW||0||1540 ± 35||Cooper et al. |
|SIM||7.4 ± 0.5||509 ± 32||Macdonald et al. , Fransson et al. (unpublished manuscript, 2011)|
|PML winter||32.0 ± 0.1a||2256 ± 12a||Macdonald et al. [1989, 1999]|
 The relative fractions of PML water (fPML), sea ice meltwater (fSIM), and river runoff (meteoric water, fMW) were then computed from the following three equations:
4.3. Evaluation of Major Controls on [CO32−] and CaCO3 Saturation State
 Here we estimate the effect of biological processes, physical mixing, and variations in salinity, and temperature on [CO32−] and the CaCO3 saturation state (ΩCa and ΩAr) in the upper 20 m in the study area. During photosynthesis, CO2 and NO3− are taken up by organisms resulting in an increase in [CO32−] and the CaCO3 saturation state of the waters. Conversely, organic matter respiration by heterotrophic microorganisms releases CO2 and NO3− to the waters, decreasing [CO32−] and CaCO3 saturation state. We use monthly variations (prefix Δ) in CT, AT, [CO32−], ΩAr, ΩCa, S, T, NO3−, fSIM and fMW, to quantitatively distinguish the effects of biological primary production (suffix bio), physical mixing (suffix mix), salinity (suffix S) and temperature (suffix temp) on the [CO32−] and the CaCO3 saturation state.
 The salinity effects on [CO32−]S, ΔΩArS and ΔΩCaS were derived from the linear correlation between the monthly change in salinity (ΔS) and AT (ΔAT) in the upper 20 m (ΔAT = 50.5ΔS + 0, r2 = 0.95, rmse = ±3 μmol kg−1). The intercept of the regression was null (±1.7 μmol/kg), meaning that salinity changes explained most of the ΔAT, and other processes, such as biological primary production made insignificant contributions. We used the slope and the [CO32−]/AT ratio to estimate the change in [CO32−] due to changes in salinity, similar to the approach adopted by Shadwick et al. [2011a].
 The effects of biological CO2 drawdown during photosynthesis on [CO32−], ΩCa, and ΩAr ([CO32−]bio, ΩCabio, and ΩArbio, respectively) were estimated from the correlation between [CO32−] and NO3− during the period of largest NO3− loss, from March to August (see section 5.2 and Figure 5e). To exclude the effect of salinity variations on [CO32−], Ω, and [NO3−], their values were normalized to a salinity of 31 ([CO32−]Snorm = 31[CO32−]/S, NO3Snorm = 31[NO3−]/S), corresponding to the annual mean value in the upper 20 m. The linear correlation between mean salinity-normalized [CO32−] and [NO3−]Snorm for this period, [CO32−]Snorm = −6.20 [NO3−]Snorm + 106.7, yielded a coefficient of determination (r2) of 0.91, and rmse on the fit of ±2.3 μmol kg−1. The slope of the fit (∼6 ± 0.7 μmol kg−1) was multiplied by ΔNO3Snorm to estimate the change in carbonate ion concentration due to biological production ([CO32−]bio). The same approach was used to derive the biological effects on ΩAr and ΩCa, using slopes from the linear correlations between ΩAr or ΩCa and [NO3−]Snorm, (slopes of −0.09, (rmse = 0.04) and −0.14 (rmse = 0.06), respectively and r2 for both fits of 0.95, Figure 2).
Figure 2. The linear regression between salinity normalized nitrate (NO3Snorm) and the calcium carbonate saturation state between March and August. The slopes of ΩCa versus NO3Snorm (ΩCa = −0.1345 × NO3Snorm + 2.6081, r2 = 0.941, black diamonds) and ΩAr (ΩAr = −0.841 × NO3Snorm + 1.627, r2 = 0.939, open pyramids) are used to derive the biological effects on ΩAr and ΩCa.
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 The [CO32−]mix, ΩCamix and ΩArmix were estimated using the monthly changes in the mixed layer depth (MLD) and the difference between [CO32−], ΩCa or ΩAr in the subsurface (ssw) and the surface (sw, upper 20 m) waters for each month, as shown for [CO32−], as an example, in equation (4). The values for [CO32−]ssw, ΩCassw, and ΩArssw were annual mean values taken from the depth below the PML layer (∼60 m, S > 32) i.e., 73 ± 12 μmol kg−1, 1.75 ± 0.3, and 1.10 ± 0.2, respectively.
where MLD is the mixed layer depth (in m) at time t (month). Since deepening of the surface mixed layer induces mixing with underlying waters, the function Θ(dMLD/dt) is equal to dMLD/dt when dMLD/dt > 0, and equal to 0 when dMLD/dt ≤ 0 (usually referred as the Heavisied function).
 The effect of temperature on [CO32−], ΩCa, and ΩAr, was inferred from the thermodynamics of the carbonate system over the temperature range of −2°C to 7°C as described by the CO2SYS chemical speciation program [Pierrot et al., 2006]. Over this small temperature range, the correlation between [CO32−] and temperature ([CO32−] = 0.542xT + 93.72, r2 = 1, rmse = 0.002), ΩCa and temperature (ΩCa = 0.012xT +2.28, r2 = 0.999, rmse = 0.001), and ΩAr and temperature (ΩAr = 0.009xT + 1.42, r2 = 0.999, rmse = 0.001). Increasing temperature leads to increased [CO32−], ΩCa, and ΩAr, and the slopes of the linear regressions were multiplied with the ΔT to estimate the temperature effects.
 To explore the effect of changes in fSIM on the Δ[CO32−], ΩCa, and ΩAr, we used the linear relationship between solely salinity-dependent changes (i.e., ΔCO32−S, ΩCaS, and ΩArS) and the monthly change in fSIM (ΔfSIM), (we did not do this analysis for fMW because it is negligible relative to fSIM). The negative correlation between Δ[CO32−]Snorm and ΔfSIM indicates that a 1% increase in fSIM leads to a [CO32−] decrease of 1 μmol kg−1 (Figure 3, r2 = 0.951, rmse = 0.28) and 0.022 and 0.014 changes in ΩCa and ΩAr, respectively (r2 = 0.951, rmseΩCa = 0.007 and rmseΩAr = 0.004).
Figure 3. The linear regression between the monthly change in salinity normalized carbonate ion concentration, Δ[CO32−]Snorm, and the monthly change in sea ice meltwater fraction, ΔfSIM, (Δ[CO32−]Snorm = −0.901x, ΔfSIM-0.04, r2 = 0.952).
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4.3.1. Error Estimates
 The magnitude of the errors (Ex) in the evaluation of the major drivers of Δ[CO32−], ΔΩCa, and ΔΩAr were derived from the sum of the rmse values for each of the individual processes n (Ex shown for Δ[CO32−] in equation (5)).
 Based on this calculation, is ±3.8 μmol kg−1, EΔΩCa = ±0.18, and EΔΩAr = ±0.19. From these estimates, relative errors are about 4%, 8%, and 14% of the absolute values of the total change in Δ[CO32−], ΔΩCa, and ΔΩAr, respectively. It is important to realize these error estimates only take into account the rmse of the functions used to estimate the drivers. This uncertainty is responsible for only part of the uncertainties in the calculations. For instance Cbiofor each month is evaluated from the correlation over the period of March to August, which may not apply to the situation in fall. Note also that the estimate of the effect of biological photosynthesis approximates only new primary production, and not total primary production, because it does not account for recycled and imported nutrients. Another limitation of our approach is that it does not consider the coupled effects of physical-biological processes on the carbonate ion change, such as physical upwelling bringing nutrients to the surface, hence affecting the biological CO2 uptake. Moreover, this calculation does not include the measurement variability in the AT and CT values or the error associated with the CO2SYS calculation of [CO32−] and saturation states. Hence, these error estimates should be considered lower limits.