The measurement of pH in saline and hypersaline media at sub-zero temperatures :

The pH on the total proton scale of the Tris-HCl buffer system (pHTris) was characterized rigorously with the electrochemical Harned cell in salinity (S) 35 synthetic seawater and S = 45–100 synthetic seawater-derived brines at 25 and 0 °C, as well as at the freezing point of the synthetic solutions (−1.93 °C at S = 35 to −6 °C at S = 100). The electrochemical characterization of the common equimolal Tris buffer [RTris = mTris/mTris‐H+ = 1.0, with mTris = mTris‐H+ = 0.04 mol kgH2O‐1 = molality of the conjugate acid-base pair of 2-amino-2-hydroxymethyl-1,3-propanediol (Tris)] yielded pHTris values which increased with increasing salinity and decreasing temperature. The electrochemical characterization of a non-equimolal Tris buffer variant (RTris = 0.5, with mTris = 0.02 mol kgH2O‐1 and mTris−H+ = 0.04 mol kgH2O‐1) yielded pHTris values that were consistently less alkaline by 0.3 pH unit than those of the equimolal Tris buffer. This is in agreement with the values derived from the stoichiometric equilibrium of the Tris-H+ dissociation reaction, described by the Henderson – Hasselbalch equation, pHTris = pKTris⁎ + logRTris, with pKTris⁎ = stoichiometric equilibrium dissociation constant of Tris-H+, equivalent to equimolal pHTris. This consistency allows reliable use of other RTris variants of the Tris-HCl buffer system within the experimental conditions reported here. The results of this study will facilitate the pH measurement in saline and hypersaline systems at below-zero temperatures, such as sea ice brines.


Introduction
High latitude oceans contribute disproportionally to the CO 2 uptake from the atmosphere (Bates and Mathis, 2009;, but these estimates are based on data generated by sampling ice-free parts of the polar oceans. A complete picture of the polar CO 2 budget must include the role of the seasonal and perennial sea ice in CO 2 cycling and air-sea exchange in these regions. Recent research has demonstrated that brine pockets in sea ice are sites of physical and biogeochemical processing that render sea ice an environment of active carbon cycling (Arrigo et al., 1997;Dieckmann et al., 2008;Gleitz et al., 1995;Miller et al., 2011aMiller et al., , 2011bMunro et al., 2010;Papadimitriou et al., 2012;Rysgaard et al., 2011;Rysgaard et al., 2007). Processes, such as primary and secondary production (Arrigo et al., 1997;Deming, 2010), mineral authigenesis, including CaCO 3 in the form of ikaite (Dieckmann et al., 2010;Dieckmann et al., 2008;Rysgaard et al., 2013), gas exchange (Miller et al., 2011a(Miller et al., , 2011bPapadimitriou et al., 2012;Papadimitriou et al., 2004), and brine drainage (Notz and Worster, 2009) have dynamic seasonal cycles in sea ice and affect the carbonate system at the ocean-air interface in high latitudes (Bates and Mathis, 2009;Bates et al., 2006;Chierici and Fransson, 2009;Dieckmann et al., 2008;Fischer et al., 2013;Miller et al., 2011b;Papadimitriou et al., 2014;Papadimitriou et al., 2013;Rysgaard et al., 2012;Takahashi et al., 2002;Yamamoto-Kawai et al., 2011;Yamamoto-Kawai et al., 2009). However, in comparison with the current advancement of our knowledge on ice-free waters of the high latitude oceans, the study of the carbonate system in sea ice has been patchy, not least because of logistical and physical-chemical complexities (Miller et al., 2015).
Sea ice is a porous medium of mostly pure ice with a small percentage by volume of brine and gas pockets (Cox and Weeks, 1983). The chemical composition of the liquid and gas phases of sea ice results from the physical-chemical changes attendant on seawater freezing, its dissolved salt and gas expulsion from the pure ice matrix, and their entrapment and physical concentration in pockets within (Cox and Weeks, 1983). Thus, sea ice brines exhibit a much wider range of salinity (S) and temperature (t) within short temporal and spatial scales than the underlying and ice-free oceanic waters. The temperature of sea ice ranges from the freezing point of seawater at the ice-water interface [t fr = −1.93°C at 1 atm total pressure and S = 35; UNESCO (1983)] to temperatures as low as −16°C, or even lower during winter, in the coldest upper parts of ice floes in contact with the atmosphere (Miller et al., 2011a(Miller et al., , 2011b accommodating hypersaline (S NN35) brines of an equivalent freezing point. For example, at −6°C, about 66% of the water is present as ice and the residual brine has a salinity of 100. The temperature range where in situ investigation of the carbonate system in sea ice would be most beneficial is between the freezing point of seawater and the temperature at which the sea ice becomes impermeable to liquid transport and material exchange with the underlying ocean. This occurs when the brine volume becomes b 5%, which occurs at − 5°C when bulk sea ice S = 5 (Golden et al., 1998).
For the investigation of the carbonate system under such S-t conditions as found in sea ice, total alkalinity (TA), total dissolved inorganic carbon (DIC), and dissolved CO 2 (as gas fugacity, fCO 2 ) measurements are possible using current methodologies and instrumentation (Miller et al., 2015) but not the measurement of pH, which is only possible thus far at above-zero temperatures and salinities up to 40. An estimate of the pH at the sub-zero temperatures and high salinities of sea ice brines can be computed from the solution of the thermodynamic model that describes the oceanic carbonate system using measurements of TA and DIC as input parameters (Brown et al., 2014;Delille et al., 2007;Gleitz et al., 1995;Papadimitriou et al., 2007;Papadimitriou et al., 2004). This requires knowledge of the dissociation constants of carbonic and boric acids at the salinity and temperature ranges of sea ice. Empirical data for these constants, however, do not exist for t b 0°C and S N 50 in natural solutions (Dickson, 1990a;Millero et al., 2006). The required extrapolation to lower temperatures and higher salinities of the non-linear S-t functions that describe the existing empirical data set can result in sizeable errors in these computations (Brown et al., 2014). With this caveat in mind, the estimated in situ pH in sea ice brines has been reported to range between 7 and 10 (Delille et al., 2007;Gleitz et al., 1995;Miller et al., 2011a;Papadimitriou et al., 2007). Finally, the use of the traditional pH measurement techniques (potentiometry, spectrophotometry) at sub-zero temperatures and high salinities is challenging because of untested electrochemical behaviour of glass electrodes used in potentiometry, lack of experimental data for the optical parameters and dissociation constants of pH indicator dyes used in spectrophotometry, and lack of suitable calibration buffers compounding the uncertainties of both potentiometric and spectrophotometric methods at sub-zero temperatures and hypersaline conditions. The range of environmental conditions for which saline pH buffers have been characterized is 0-40°C and S = 20-40 for the 2-amino-2-hydroxymethyl-1,3propanediol (Tris) compound in synthetic seawater (DelValls and Dickson, 1998), as well as 5-45°C and S = 35 for 2-amino-2-methyl-1,3-propanediol (Bis), tetrahydro-1,4-isoxazine (Morpholine), and 2-amino-pyridine (Aminopyridine) , all on the total proton scale. Similarly, pH indicator dyes have typically been characterized at above-zero temperatures and S b 40 conditions on the total and free proton scales (e.g., Liu et al., 2011;Robert-Baldo et al., 1985), with a further extension of the dye data set on the free proton scale in NaCl solutions by Millero et al. (2009) to the full ionic strength spectrum up to NaCl saturation (0.03 b I b 5.50 m) at above-zero temperatures. Overall, there is currently no validated method for measuring pH at sub-zero temperatures or, especially, in the coupled sub-zero temperature and high salinity of sea ice brines, or at any temperature for S N 40 in multi-electrolyte media.
The aim of this work was to enable reliable measurement of pH in saline and hypersaline media at sub-zero temperatures. To this end, we determined the pH of Tris buffer solutions in corresponding salinity and temperature conditions. For this task, we extended the standard electrochemical protocol for pH buffer characterization to international standards in the Harned (hydrogen gas/silver/silver chloride) cell (Bates, 1973) described in the oceanographic pH literature (Campbell et al., 1993;DelValls and Dickson, 1998;Dickson, 1990aDickson, , 1990bMillero et al., 1993). The electrochemical characterization of pH buffers is an essential first step in the characterization of pH indicator dyes for use in the spectrophotometric pH determination. The characterization of the pH indicator dye meta-Cresol Purple (mCP) with a microfluidic flow spectrophotometric cell in the same temperature and salinity ranges will be reported in a companion paper. The results relayed here will therefore promote the acquisition of high quality in situ measurements of pH in polar waters and sea ice brines, and will improve the confidence in future investigations of this parameter of the carbonate system in these environments.

Methods
The pH of equimolal and non-equimolal Tris buffers (pH Tris ) in synthetic seawater and brines was determined with the electrochemical Harned cell (Bates, 1973), the only rigorous method available for the characterization of primary buffer solutions (IUPAC, 2002). The characterization was conducted in the Marine Physical Laboratory, Scripps Institution of Oceanography, University of California, San Diego, USA. The determination of the pH Tris requires the determination of the standard potential of the Harned cell from e.m.f. measurements with pure HCl solutions, HCl solutions prepared in the synthetic medium, and in HCl solutions in the synthetic medium with Tris. Details of the all-glass type Harned cell, and the silver-silver chloride and hydrogen electrodes used in this study can be found in DelValls and Dickson (1998). The solutions were analysed in duplicate or triplicate at each HCl molality in the Harned cells in a thermostated water-glycol bath. The bath temperature was controlled to 0.01°C and all e.m.f. measurements were corrected to 1 atm hydrogen gas fugacity (DelValls and Dickson, 1998 strength multi-electrolyte solutions matching the ionic ratios of standard seawater and seawater-derived brines. The synthetic solutions were prepared gravimetrically using the recipe in Table 1, which was based on that of standard seawater (S = 35) in DelValls and Dickson (1998). All synthetic solutions were prepared with purified salts, to maximize stability in the electrochemical response of the Harned cell. All salts (NaCl, Na 2 SO 4 , KCl, CaCl 2 , MgCl 2 ) were twice re-crystallized from reagent grade salts, air-dried, annealed at 200°C, and (except for CaCl 2 and MgCl 2 ) were heated to 500°C (10 h) (Dickson, 1990a;Millero et al., 1993). The CaCl 2 and MgCl 2 salts were used to prepare approximately 1 mol kg solution -1 Ca 2+ and Mg 2+ working stock solutions, ) of the salts in synthetic brines of salinity S N 35 and ionic strength I S was calculated as m S = m 35 I S /I 35 , with I S = 19.9184 S/(1000-1.00198 S) (DelValls and Dickson, 1998). The concentration in mol kg solution which were used for the preparation of the synthetic media. The concentration of Ca 2+ and Mg 2+ in these stock solutions was determined gravimetrically with a relative standard deviation better than 0.1% by Mohr titration with 0.3 mol kg solution -1 AgNO 3 , itself standardized similarly against purified NaCl and KCl (Dickson, 1990a;Millero et al., 1993). The working stock HCl solution (approximately 1 mol kg solution -1 ) was prepared gravimetrically with de-ionized water from double-distilled 6 M HCl solution. The concentration of these HCl solutions was determined by coulometry with a relative standard deviation better than 0.001%. It is standard practice to adjust the e.m.f. measurements in synthetic salt solutions so that their standard potential corresponds to that of Bates and Bower (1954). The adjustment factor is determined from e.m.f. measurements in dilute HCl solutions as described in the next section.

The standard potential of pure HCl solutions
The standard potential (E o = e.m.f. at infinite proton dilution) of the cell was determined regularly to ensure conformity with the measurements by Bates and Bower (1954). The   Table S1 in Supplementary Information for cells (B) and (C) and in Table 3 for cells (D) and (E); these cells are described in the next two sections. In this case, instead of the free proton scale (m H +), the total proton scale has been used previously, defined as m H + T = m H + + m HSO 4 − = m H +(1 + m SO 4 2−/K HSO 4 −), with m H + T =m HCl = m 1 in cells (B) and (C) above (Campbell et al., 1993;Dickson, 1990b). Thermodynamically rigorous, the total proton scale is suitable for the determination of acidity constants (Dickson, 1990b) and, as per objective of this study, is also used here to define and determine the pH of Tris buffers in keeping with previous studies (Campbell et al., 1993;DelValls and Dickson, 1998). Conversion to the free proton scale requires knowledge of K HSO 4 −, which is not available at below-zero temperatures. It is beyond the scope of this study to determine K HSO 4 − because it is not needed to determine acidity constants in the total proton scale; as outlined below, this parameter is incorporated in the determined E o ⁎ term of the Nernst equation for cells (B) and (C). (Campbell et al., 1993;Dickson, 1990b;Millero et al., 1993). Here, E o , k, and γ ±HCl are as explained in the previous section, K HSO 4 − and m HCl as above, m SO 4 2− = total sulphate molality, m Cl − = total chloride molality, and E = measured e.m.f. in cells (B) and (C) above adjusted by ΔE o BB .
The value of E o ⁎ =E o -2klnγ ±HCl +kln(1+m SO 4 2−/K HSO 4 −) is determined at each temperature and salinity at m HCl → 0, the standard state of infinite dilution in the pure medium, as the intercept of the quadratic function, E′ = E+kln(m HCl m Cl −) = a + b m HCl + c m HCl 2 , with E o ⁎ = a (Campbell et al., 1993;Dickson, 1990b). The adjusted e.m.f. measurements in synthetic solutions of several different HCl molalities (n = 5-6) at each salinity and temperature (given in Table S1 in Supplementary Information) were used to obtain E′. The experimental E′ values were fitted to a quadratic function of m HCl with least-squares regression in Excel (shown for S = 35 and 45 in Fig. 1) to obtain E o ⁎ and its standard error (equivalent to that of the intercept of the quadratic fit), which are both given in Table 2 The freezing point of the synthetic brines was computed from the inversion of the empirical absolute salinity-temperature (S A -t) relationship of sea ice brines at ice-brine equilibrium, S A = 1000 (1-54.11/t) −1 (Assur, 1958).

Determination of the pH Tris in synthetic seawater (S = 35) and synthetic brines (S N 35)
The values of E o ⁎ in cells (B) and (C) ( , yielding a molality ratio, R Tris =m Tris /m Tris−H + = 0.5. To examine the internal consistency of the e.m.f. measurements in these non-equimolal Tris-HCl buffers, their pH was also computed from the equimolal pH Tris , when available, and their R Tris using the Henderson -Hasselbalch equation (Pratt, 2014), pH Tris =pK Tris ⁎ + logR Tris , which is derived from the stoichiometric equilibrium of the Tris-H + dissociation reaction (Millero, 2009), with pK Tris ⁎ equivalent to the equimolal pH Tris when R Tris = 1.
The E o ⁎ and pH Tris data from this study alone and combined with relevant data at above-zero temperatures from earlier studies were fitted to non-linear equations of temperature and salinity or ionic strength using the Regression function in the Data Analysis Tool of Excel. The fitted coefficients of these equations, along with the adjusted squared correlation coefficient (r 2 ) and the standard error of the fit (σ fit ), as well as the number of fitted observations (n), are all reported from the Regression output in subsequent sections. Information about the standard error of the individual fitted coefficients is reported in Tables S2 and S3 in Supplementary Information.

Results
The focus of this study was the characterization of the pH of Tris buffers at below-zero temperatures but e.m.f. measurements were also obtained at 25 and 0°C for evaluation relative to the existing datasets at overlapping temperature and salinity ranges. We kept this

Table 2
The apparent standard potential (E o ⁎ ) and its regression standard error (σ Eo ⁎ ) (both in V) of cells (B) and (C). Values in italics were derived from the salinity and temperature extrapolation of Eqs. (15) and (16) in Dickson (1990b) and Eqs. (17) and (18) with the coefficients derived from the combined data sets in Campbell et al. (1993). protocol throughout the experimental salinity range (35-100) and report the results at 25 and 0°C here in order to provide data useful for occasions in sea ice studies when pH measurement at sub-zero temperatures is not possible due to harsh field conditions and restrictions by equipment or method.
6.1. The standard potential of the Harned cell to the freezing point of synthetic seawater and brines The E o ⁎ values at each experimental temperature and salinity along with their standard error are given in Table 2 and are shown in Fig. 2. The e.m.f. measurements at S = 35 (Fig. 1a,b) were consistent with published data at 25 and 0°C (Campbell et al., 1993;Dickson, 1990b;Khoo et al., 1977), while those made at S = 45 (Fig. 1c,d) were consistent with the values in Khoo et al. (1977) at 25°C. The current E o ⁎ values at 25 and 0°C and S = 35 and 45 were different by b+0.00030 V from previous determinations in these conditions (Campbell et al., 1993;Dickson, 1990b). No other direct comparison is possible as the remainder of the current data extend beyond the temperature minimum and salinity maximum of the previous data sets. An indirect comparison can be made using the extrapolation of the ionic strength and temperature function of E o ⁎ in Dickson (1990b) and in Campbell et al. (1993). This will also allow a direct evaluation of the extrapolation as practiced by necessity so far by sea ice scientists.
The current E o ⁎ values at below-zero temperatures and S = 35 were +0.00010 to +0.00020 V and +0.00060 V different from those predicted by extrapolation of the equations in Dickson (1990b) and Campbell et al. (1993), respectively (Table 2). These differences are equivalent to 0.002-0.011 pH unit for the Tris buffer in synthetic seawater. A revised non-linear function of temperature is given below for E o ⁎ in synthetic seawater (S = 35) from the regression fit to the combined past and current data from 55 to −1.7°C (r 2 = 0.99995, p b 0.00001, n = 27, σ fit = 0.00004 V; the fitted residuals are shown in Fig. S1a in Supplementary Information), with E o = the Bates and Bower (1954) standard potential of the Harned cell as fitted by Dickson (1990b) and T = temperature (in K): The difference between the current E o ⁎ values in the synthetic brines (S ≥ 45) and the extrapolated values from the existing equations (Table 2) ranged from +0.00020 to +0.00670 V (equivalent to 0.003-0.118 pH unit), increasing with increasing salinity throughout the experimental temperature range (Fig. 2). The current measurements provide for a more accurate and reliable measurement of the pH in ice-brine systems. To facilitate this application, we combined the E o ⁎ value at the freezing point of seawater derived from Eq. (1) above (E o ⁎ = 0.25540 V at −1.93°C and S = 35 at 1 atm total pressure) with the values obtained at the different freezing points of S ≥ 45 brines (Table 2) to obtain a best-fit temperature function of E o ⁎ applicable to thermally equilibrated sea ice brines. We found E o ⁎ to be best described (r 2 = 0.98906, p = 0.00005, n = 7, σ fit = 0.00015 V; the fitted residuals are shown in Fig. S1b in Table 3 The potential (E Tris , in V) of cells (D) and (E) with Tris buffer solutions in synthetic seawater and brines. The E Tris is the value after adjustment by ΔE o BB (in V) so that the standard potential of the cells corresponds to that of Bates and Bower (1954) [see Methods and DelValls and Dickson (1998)  Supplementary Information) by a quadratic function of temperature (T, in K) at the freezing point of seawater and seawater-derived brines from −1.93 to −6.00°C (S = 35-100): An extended equation is provided below for the computation of E o ⁎ by interpolation at any salinity and temperature outside the restricted conditions of Eqs. (1) and (2) above but within the limits of the experimental range. The interpolation will be useful for the characterization of pH buffers (on the total proton scale) on such occasions. Although the current E o ⁎ data set is sparse as a function of temperature, it was combined with the data sets in Dickson (1990b) and Campbell et al. (1993) for an overall best fit (r 2 = 0.99186, p b 0.00001, n = 133, σ fit = 0.00008 V) in the function format of the previous studies in ionic strength (I, in molality) and temperature (T, in K), with E o from Dickson (1990b) as before: In the above equation, the ionic strength was calculated as a function of salinity as described in Table 1 Table 2 for observed values).

The pH of Tris buffers to the freezing point of synthetic seawater and brines
The pH values of the equimolal Tris buffer are listed in Table 3 and are shown in Fig. 4. The equimolal pH Tris in synthetic seawater at 25°C and 0°C from the observed E o ⁎ (Table 2) and the e.m.f. measurements in cells (D) and (E) ( Table 3) was within 0.002 pH unit from the values computed from the salinity and temperature function in DelValls and Dickson (1998) based on their experimental measurements at S = 20-40 and 0-45°C. The equimolal pH Tris in synthetic seawater at subzero temperatures differed by 0.000-0.004 pH unit from the values obtained from the extrapolated DelValls and Dickson (1998) The equimolal pH Tris in synthetic brines (S ≥ 45) was determined up to S = 70. It was within 0.007 pH unit at S = 45 and 50 from the values predicted from the extrapolation of the DelValls and Dickson (1998) function but was lower than the extrapolated values by 0.009-0.019 and 0.021-0.036 pH unit at S = 60 and 70, respectively, at all examined temperatures, suggesting increasingly unsuitable values from extrapolation at high salinities regardless of temperature (Fig. 4). Combining the value of the equimolal pH Tris at the freezing point of S = 35 seawater from Eq. (4) above (equimolal pH Tris = 9.0039 at −1.93°C) with the observations obtained at the different freezing points of S ≥ 45 brines (Table 3), the equimolal pH Tris at ice-brine thermal equilibrium was found to be best described (r 2 = 0.99929, n = 9, p b 0.00001, σ fit = 0.002 pH unit; the fitted residuals are shown in Fig. S2b in Supplementary Information) to −4°C and S = 70 by the following function of temperature (T, in K): pH Tris equimolal ð Þ¼-300435:6052 þ 7240100:99 T −1 -99:5850583 T þ 53678:964954 lnT; The non-equimolal pH R Tris =0.5 values are given in Table 3 and are shown in Fig. 4. On the occasions when both the equimolal and the non-equimolal buffers were measured (35 ≤ S ≤ 70), the non-equimolal pH R Tris =0.5 values were within 0.001 pH unit from those determined from the Henderson -Hasselbalch equation described in the earlier section Determination of the pH Tris in synthetic seawater (S = 35) and synthetic brines (S N 35). The pH R Tris =0.5 at the freezing point was determined for 50 ≤ S ≤ 100 and −6.0°C ≤ t ≤ −2.8°C. The best-fit function of temperature (T, in K) for the non-equimolal pH R Tris = 0.5 in the temperature and salinity conditions of thermally equilibrated seawater-derived brines is as follows (r 2 = 0.99991, n = 13, p b 0.00001, σ fit = 0.001 pH unit; the fitted residuals are shown in Fig As mentioned at the beginning of the Results section, there can be occasions when the measurement of pH in cold media, such as sea ice brines, may not be possible at below-zero temperature. To provide interpolation power for these occasions, the data sets of the equimolal pH Tris from this study and the study of DelValls and Dickson (1998) were combined to obtain a best fit in the format of the latter study, valid at temperatures (i) between 0 and 45°C for S b 35, (ii) between the freezing point and 45°C for 35 ≤ S b 45, and (iii) between the freezing point and 25°C for 45 ≤ S ≤ 70. The best fit equation in salinity (S) and temperature (T, in K) (r 2 = 0.999995, n = 273, p b 0.00001, σ fit = 0.001 pH unit; the fitted residuals are shown in Fig. 5a, c) At 25°C and S = 35, Eq. (7) yields pH Tris (equimolal) = 8.094, while at −4°C and S = 70, pH Tris (equimolal) = 9.191 (see Table 3 for observed values). The equivalent overall fit on the current limited nonequimolal pH R Tris =0.5 data set yielded the following function of salinity and temperature (T, in K) at 50 ≤ S ≤ 100 and from the freezing point of such brines to 25°C (r 2 = 0.99999, n = 41, p b 0.00001, σ fit = 0.002 pH unit; the fitted residuals are shown in Fig. 5b Using Eq. (8) above, the predicted pH R Tris =0.5 = 8.637 at 0°C and S = 35, and pH R Tris =0.5 = 8.664 at 0°C and S = 45. These values were within 0.004 pH unit from the measured values (Table 3), and so it is reliable to extend Eq. (8) to these salinities.

Discussion
The investigation of the carbonate system in oceanic waters and the determination of the potential for air-sea CO 2 exchange have intensified in an attempt to understand the implications on global climate of the increase in the atmospheric CO 2 since the industrial revolution. The required sampling and analytical protocols have been improved through continual method and instrument development, allowing dense sampling in space and time for any pair of the 4 measurable parameters of the carbonate system (TA, DIC, pH, fCO 2 ) (DOE, 1994;Hales et al., 2004;Liu et al., 2011). While the measurement of all 4 parameters is now routine in open ocean waters (e.g., Millero et al., 2002), including polar waters (Bates and Mathis, 2009;Bates et al., 2006), the same is not true for oceanic environments at sub-zero temperatures, such as sea ice. At the salinity and temperature conditions in sea ice brines, the concentrations of TA and DIC, as well as fCO 2 naturally cover large ranges controlled by the physical concentration of seawater solutes during the freezing of seawater and further cooling of internal sea ice brines, dilution of brine solutes by meltwater during sea ice melt, biological activity, CaCO 3 precipitation and dissolution, and CO 2 gas exchange (Delille et al., 2007;Dieckmann et al., 2008;Gleitz et al., 1995;Miller et al., 2011aMiller et al., , 2011bMunro et al., 2010;Papadimitriou et al., 2012;Papadimitriou et al., 2007;Papadimitriou et al., 2004). By extension, large variations in brine pH can also be expected in such environments, but there is only rudimentary knowledge of pH changes in sea ice as direct determination of this parameter has been hampered by lack of characterized calibration standards (buffers, indicator dyes) and unsuitable analytical set-ups for the sub-zero temperatures and, in the case of internal sea ice brines, highly saline conditions (S N 35).
Currently, the pH measurement protocols in sea ice and sub-zero temperature oceanic waters, restricted by the temperature limitation of both buffers and technique, have only been capable of pH measurements at (constant) above-zero temperature. For example, Delille et al. (2007) used commercial glass electrodes and high salinity Tris and Aminopyridine buffers for instrument calibration on samples returned  Table 3 in this study (+) and as computed from the results for the m Tris = m Tris-H + = 0.04 mol kg -1 buffer in Table 2 of DelValls and Dickson (1998) to the laboratory and maintained at 1-3°C, and so did Gleitz et al. (1995) at 20-22°C using NBS standard buffers. Miller et al. (2011a) used the spectrophotometric technique with un-purified mCP as the pH-sensitive indicator dye at 25°C, as did Hare et al. (2013) at 0°C. A technique based on the pH-sensitive fluorescence properties of acridine and harmine has been developed and applied to fresh and salty ice surfaces, but solely for monitoring rather than quantification of pH, due to lack of suitable characterization and calibration of the fluorescence properties of these probes (Wren and Donaldson, 2012).
In this study, we electrochemically characterized the pH T (total proton scale) of Tris-HCl buffers using the Harned cell, the only rigorous method available for the task (IUPAC, 2002). Use of these buffers can facilitate the calibration of the analytical pH instrumentation at the experimental temperature and salinity ranges of this study. The pH T of the Tris-HCl buffers was increasingly alkaline with increasing salinity at constant temperature and with decreasing temperature at constant salinity (Table 3; Fig. 4). The equimolal Tris buffer covered a pH T range from 8.09 at S = 35 and 25°C to 9.19 at the freezing point of an S = 70 synthetic brine (−4°C) ( Table 3). The pH T of the non-equimolal (R Tris = 0.5) Tris buffer ranged from 8.63 at S = 35 and 0°C to 9.06 at the freezing point of an S = 100 synthetic brine (−6°C) ( Table 3) and was 0.3 pH unit less alkaline than its equimolal counterpart (Fig. 4) as predicted using the stoichiometric Tris-HCl equilibrium and the Henderson-Hasselbalch equation. On the strength of this evidence and the study of Pratt (2014) in synthetic seawater, Tris-HCl buffers of varying R Tris and, hence, pH T can be prepared if needed with the protocol outlined in Methods, and their pH T can be estimated reliably with the Henderson-Hasselbalch equation and the data presented here for investigations within the temperature and salinity ranges of this study.
The pH T ranges for the equimolal and non-equimolal (R Tris = 0.5) Tris buffers covered the alkaline spectrum of pH estimates at in-situ (below-zero) temperatures in sea ice. Delille et al. (2007) reported pH T values ranging from 8.4 to 9.4 in Antarctic fast ice brines (S = 24-89). In sackhole brines from the Weddell Sea, Antarctica, Papadimitriou et al. (2007) determined a pH SWS (seawater proton scale) range of 8.4 to 8.8, while Gleitz et al. (1995) reported a pH SWS range of 7.8 to 9.9. Hare et al. (2013) reported pH T values between 7.1 and 9.5 in frost flowers, bulk ice cores, and brines from artificial sea ice grown at an outdoors experimental facility. In the Arctic Ocean, pH T ranged from 7.7 to 12.1 in frost flowers and sea ice brines (Fransson et al., 2013), and from 8.3 to 8.5 (free proton scale, pH F ) in sackhole brines (S = 68-163) (Miller et al., 2011a) in the Amundsen Gulf, while Rysgaard et al. (2012) reported pH T values between 9.9 and 10.1 in sea ice meltwater. In all these previous field studies, the pH values at in situ (below-zero) temperatures have been computed from measured TA and DIC in sea ice environments (Brown et al., 2014;Papadimitriou et al., 2009;Papadimitriou et al., 2007) or from the pH measured directly in the sea ice medium at above-zero temperatures and either TA or DIC (Brown et al., 2014;Delille et al., 2007;Fransson et al., 2013;Gleitz et al., 1995;Hare et al., 2013;Miller et al., 2011a). In those instances, the pH at in situ (below-zero) temperatures has been derived by solving the system of equations that describe the thermodynamic relationships of the marine carbonate system (DOE, 1994) but with the caveat that the relevant equilibrium constants have not yet been characterized at sub-zero temperatures. Therefore, the use of this approach and the derived pH at the in situ (below-zero) temperatures rely on extrapolation of the existing oceanographic salinity and temperature functions of the equilibrium constants with discouragingly large uncertainties (Brown et al., 2014).
The electrochemical characterization of the Tris buffer system in this study enables the spectrophotometric characterization of pH indicator dyes in seawater-based hypersaline media at below-zero temperatures. Both techniques and their results will free the sea ice biogeochemical community from the uncertainty in the measurement of pH in sea ice by affording investigators direct pH determination in sea ice brines down to −6°C and salinity 100. Sea ice has been found to become impermeable at a porosity b 5% (as relative brine volume), coincident with a sea ice temperature of −5°C at a bulk sea ice salinity of 5 (Cox and Weeks, 1975;Golden et al., 1998), or colder in more saline bulk sea ice, and vice versa, based on the phase relationships in the medium (Cox and Weeks, 1983). Hence, sea ice in the current experimental temperature range (−2 ≤ t ≤ −6°C) is permeable to material transport via the brine channels. As a result, the current experimental conditions are pertinent to the study of the exchange potential of the brine carbonate system in sea ice with the underlying ocean and the atmosphere above.
Major compositional changes in the internal brine in sea ice will occur at temperatures well below −6°C as a result of extensive precipitation of hydrated salts, such as mirabilite, gypsum, and hydrohalite (Butler et al., 2016;Butler and Kennedy, 2015;Marion, 2001). Consequently, a different logistical approach is required for the study of the brine carbonate system in the coldest compositional spectrum in sea ice, which is nearest to the atmosphere. Further work below the minimum temperature presented here must take into account mineral dynamics in sea ice for the determination of the chemical composition of the internal brines, which will inform the composition of synthetic or natural solutions to be used in the laboratory for the characterization of pH buffers and indicator dyes.

Conclusions
The current data set established explicitly the value of one of the important parameters in the study of the carbonate system, the pH of the Tris-HCl buffer system, in sub-zero temperature saline environments and within international standards. The pH of the Tris buffer was fully characterized on the total proton scale in the temperature range from 25°C to the freezing point of S = 35 seawater (freezing point: −1.93°C) and seawater-derived brines up to a salinity of 100 (freezing point: −6.0°C). The difference between measurements at sub-zero temperatures and the extrapolated values computed from the existing above-zero temperature data sets may be negligible at S = 35 in terms of both the apparent standard potential of the electrochemical Harned cell and the equimolal pH Tris but increased systematically with increasing salinity at all temperatures. Based on the apparent standard potential of the Harned cell, this discrepancy was found to be equivalent to 0.118 pH unit at the highest salinity investigated here (S = 100), a substantial deviation with consequent discrepancies in other parameters of the carbonate system derived from it relying on extrapolation of existing electrochemical and oceanographic data sets defined for above-zero temperatures and S = 0-50. Hence, the current data will provide considerable improvement in the study of pH in cold saline and hypersaline conditions relative to the only choice of extrapolation available until now to biogeochemists. For a more complete characterization of the carbonate system in the cryosphere, the dissociation constants of its weak acids and bases (e.g., carbonic and boric acids) must be determined at below-zero temperatures.