VERIFICATION OF PH FLUCTUATIONS IN NARRAGANSETT BAY

In order to understand potential changes in pH driven by increasing atmospheric carbon dioxide, we first need to understand what controls pH and its variability in estuaries today. We measured total alkalinity, dissolved inorganic carbon, pH, temperature and salinity of samples taken hourly for 24 hours once a month at three sites in Narragansett Bay (2/2010 to 4/2011) to understand the controls on daily and seasonal pH variation: GSO, Greenwich Bay (GB), and Potter Cove (PC). We also measured in situ pH (pHe ) and temperature every five minutes at the same sites and during the same time periods. Our calculations of pH (pHc) from total alkalinity, dissolved inorganic carbon, salinity and temperature measurements indicate daily pH variation of 0.10 to 0.62. The largest pHc range for GSO was on April 1 st 2010, which had range of pHc of 8.36 to 7.94. The pHe range on the same day was from 8.19 to 8.01. The largest pHc range for PC was on March 8 th 2011, which had range of pHc of 8.68 to 8.16. The pHe range on the same day was from 9.02 to 8.46. The largest pHc range for GB was on May 13 th 2010, which had range of pHc of 8.04 to 7.42. The pHe range on the same day was from 7.91 to 7.52. We propagate errors in our calculations and use a conservative mixing model to determine if this variation in pH is valid or an artifact of error. The variations in pH are real and are not an artifact because the observed daily range in pH is greater than the pH range due to total error. We compared pH determined from dissolved inorganic carbon and total alkalinity measurements to pH determined from a conservative mixing model. The comparisons show that daily pH variation is not completely explained by the mixing of waters with different salinity, alkalinity, and dissolved inorganic carbon. Shortterm pH change that cannot be explained by the model and have carbon dioxide and dissolved oxygen deviation from equilibrium are driven by biological activity, primarily photosynthesis and respiration. The fractional departure of dissolved carbon dioxide (([CO2 * ] –[CO2 * ]sat)/[CO2 * ], CO2* = dissolved and hydrated CO2) and dissolved oxygen (([O2] – [O2]sat)/[O2]) are anti-correlated, but not clearly linked to chlorophyll concentration. The mixing efficiency of the estuary provides a physical explanation as to why pH below equilibrium concentrations of CO2 co-varies with low dissolved oxygen concentrations.


INTRODUCTION
When gas phase carbon dioxide (CO 2 ) dissolves in seawater and is hydrated, it forms carbonic acid and readily dissociates into bicarbonate and hydrogen ion, decreasing the pH of seawater. If anthropogenic CO 2 emissions continues to increase at a rate of 1% per year, the average pH of the surface ocean is predicted to fall 0.3 to 0.4 pH units by 2100 (Haugen and Drange 1996;Brewer 1997

Conceptual Background
The fundamental assumption in a conservative mixing model is that there is chemical continuity when river and ocean water are mixed. Since the carbonate system inhibits the degassing or evasion of CO 2 compared to a non-reactive gas, such as dissolved oxygen (DO) (Williams and Follows 2011), a conservative mixing model approach can be applied to determine the cause of pH change in an estuary (Cai et al. 1998, Boyle et al. 1974. Consider a quantity of river water with a known mass (M r ), salinity, S r , and alkalinity, TA r mixed with a quantity of ocean water with a known mass (M o ), salinity, S o , and alkalinity, TA o : where f r and f o are the proportions of freshwater and seawater respectively. The second approach is to evaluate whether the observed pH changes are well explained by physical and biological processes. This approach requires understanding how changes in the environment lead to a change in pH. Salinity, temperature, TA, and DIC are often used to study how changes in an estuarine environment affect the carbon dioxide system (e.g. Jung et al. 2008, Wang andCai 2004;Cai et al. 2000).
However, TA and DIC are not always conservatively mixed in an estuary. Benthic respiration, in the form of sulfate reduction or nitrification, generates DIC and TA (Jiang et al. 2008;Krumins et al, 2013) and consumes dissolved oxygen (Abril 2001;Cai et al. 2011). Photosynthesis consumes DIC and produces dissolved oxygen. It does not affect TA in an environment predominately buffered by the carbonate system within a pH range of 7 to 9 (Morel and Hering 1993). If the pH change at a site cannot be attributed to conservative mixing and the concentration of dissolved oxygen is above or below a concentration if it were at equilibrium with the atmosphere, the pH change can be attributed to biological activity.

Study Sites
Narragansett Bay ( Figure 1) is a partially to well-mixed estuary that receives water from the Rhode Island Sound (RIS) and a variety of small rivers; its circulation is dominantly driven by wind and tidal forcing (Kincaid et al. 2002). The bay is rectangular with an area of 328 km 2 (Pilson 1985) and has a drainage basin of approximately 4,700 km 2 (Ries 1990). It has a north-south decreasing salinity gradient.
The northern portion of the estuary is shallow, with a mean depth that ranges from 7.6 to 8.3 meters (Pilson 1985). The depth increases considerably at the mouth (~37 m).
The salinity range of waters that enter the Bay from RIS is typically 31 to 33.5 g kg -1 (Pilson 1985). The main freshwater discharges into the upper bay are the Blackstone and Pawtucket Rivers, as well as the Taunton River via Mount Hope Bay (Spaulding and Swanson 2008). The Taunton, Blackstone, and Pawtuxet Rivers contribute 75% of the freshwater to the bay; the rest is from minor tributaries (Ries 1990).
Groundwater is not thought to be a significant source of freshwater to the bay (Pilson 1985, Ries 1990

Chemical Analyses
We measured TA using an open-cell titration with a semi-automatic titration system (Metrohm 809 Titrando) fitted with syringe pumps and a high-precision pH meter (Metrohm pH Electrode Model 6.0234.100). The samples were titrated to 210 mV, which is approximately a pH of 4. TA was determined using the slope and intercept values of the Gran titration curve (Edmond, 1970). We measured DIC by extraction and infrared (IR) measurement of purged CO 2 using an Automated Infra Red Inorganic Carbon Analyzer (AIRICA) system. The AIRICA system acidifies and strips the CO 2 out of a known volume of seawater ranging from 500 µL up to 2000 µL and integrates the infrared absorbance from CO 2 . The AIRICA system consists of 4 main components: a syringe module, a sample stripping manifold, a LICOR LI-7000 non-dispersive CO 2 infrared analyzer and a personal computer. Although the peak area is measured three times per sample, only the mean of the last two measurements is used, to avoid any carryover effect between samples. The peak area of the sample compared to that of the standard is used to determine the sample's DIC concentration.
We measured chlorinity by silver nitrate titration following IODP Technical Note 15 Protocol using a 1 M silver nitrate solution (Gieskes et al. 1991

Quality Control and Assurance
From August 2010 to May 2011, we took replicates of the samples for the first measurement in each 24hour period to determine the uncertainty associated with sampling. We used a solution with a known mass of dissolved borax as an internal consistency test for the TA measurements. We measured the TA of the borax solution at the beginning, middle, and end of each subsampling set of TA measurements.

Error Analysis
We determined the uncertainty for TA from analysis of the standard deviation of sample replicates and borax solutions. Pooled standard deviations were first calculated and propagated to determine the relative uncertainty due to analysis, handling, and storage (Dickson 2007). We determined the analytical uncertainty for DIC by taking the difference between the two peak area measurements of each sample from a set of (i) 10 randomly chosen 24 hour sampling set and (ii) 10 randomly selected Dickson standard measurements for CRM 94, 100, and 102. We then propagated the uncertainty determined from the peak area with the uncertainty determined from the sample replicates to obtain the relative uncertainty due to analysis, handling, and storage. We determined the uncertainty of the salinity measurements from the standard deviation of the titration volume of silver nitrate used to determine the chlorinity (and subsequently salinity) of the standards.
We calculated the maximum error range for the calculated pH of each sample (pH rer ) to compare the variability of the calculated parameters due to error to the daily range of the parameter. The motivation of this calculation is to determine the sensitivity of the calculated parameters to errors in salinity, DIC, TA, and temperature measurements. The errors can be correlated or not correlated. If the errors of DIC and TA measurements are not correlated, the total error propagation in calculated pHc is ± .0062 if the accuracy of DIC and TA is assumed to be ± 2 µmolkg -1 and ± 4 µmolkg -1 (Zeebe and Wolf-Gladrow 2011). In this study, we calculate the worst-case scenario, as if the errors of DIC, TA, salinity, and temperature were correlated.

Parameter calculation
We calculated pH and associated parameters (Revelle factor, B=( ), (pCO 2 ), and the degree of saturation of calcite and aragonite Ωc and Ωa, respectively, Appendix B) using the program CO2SYS . We used carbonate dissociation constants from Cai and Wang (1998). These dissociation constants are appropriate for the salinity ranges in this study (17.89 to 31.71 gkg -1 ) and allow us to determine a pH value from the DIC and TA on the NBS pH scale. RIDEM and NBNERR calibrate their pH electrodes using NBS buffers. The values of K sp for calcite and aragonite are from Mucci (1983).

Conservative Mixing Model
The mixing model assumes that salinity, TA, and DIC are conservatively mixed. A substance is conservatively mixed when the plot of its value against salinity is linear (e.g., Boyle et al. 1974, Liss 1978, Cai et al. 2010). Non-conservative behavior is characterized by a non-linear relationship of the constituent with salinity (Boyle et al. 1974). When a property is conservatively mixed, the temporal variability of its end members' compositions is not important, as long as the average is constant over the flush time of the estuary (Loder andReichard 1982, Sharp et al. 1982). TA is thought to be mixed conservatively in Narragansett Bay (Magnuson 1997;Boucher 1991).
For this modeling exercise, we assumed all freshwater inputs to be from rivers and runoff, since groundwater inputs to Narragansett Bay are smaller than riverine inputs (Ries 1990). We calculated pH based on the proportion of freshwater and seawater. pH calculated from TA and S is temperature-dependent. The model requires the temperature of the river (t r ) and ocean (t o ) end members, or a final temperature (t f ).
We determined the final temperature of the mixture by assuming adiabatic mixing. In addition to the conservative mixing of TA, DIC, and salinity we considered a scenario at which: (1) t r and t o are the same temperature, (2) t r and t o are different temperatures using the following equation: That is, the TA, DIC, and salinity depend on the relative contributions of the river end-member (Ta r , DIC r , S r ) and the ocean end-member ( To quantify pH change that is non-conservative with respect to DIC and not due to biological activity, we calculated pH if it were in equilibrium with the atmosphere and compared it to pH determined from conservative mixing. We determined pH at equilibrium with the atmosphere (pHeq) from the partial pressure of atmospheric CO 2 and water properties (salinity, TA, temperature). The pH of the conservative mixing line is not equal to pHeq because the mixing model assumes that DIC is not lost or gained due to gas exchange. Therefore, pHeq at 25 o C should be greater than the pH of the conservative mixing line at 25 o C. Conversely, pHeq at 5 o C should be lower than the 5 o C pH mixing line. Other factors that can contribute to the difference between pHeq and the pH of the mixing line are (i) temporal variation in the end-members being mixed, such as events with significantly lower river alkalinity (e.g., runoff from acid sulfate soils, Cornfield 2000) and (ii) processes that generate alkalinity within the estuary (e.g., removal of sulfate from the water column by sulfate reduction coupled to pyrite precipitation, Gallagher et al. 2012, Krumins et al. 2012.

Monthly data in Narragansett Bay
TA and salinity are strongly correlated at all sites ( Figure 2a). DIC and salinity are less strongly correlated (Figure 2b), indicating that DIC is non-conservative. TA and DIC are most strongly correlated at GSO and less so at GB (Figure 2c). At all sites, the days with the minimum values of salinity, TA, and DIC coincided with days with the largest ranges. Our March and April 2010 data from GB and GSO exhibit the lowest salinity, DIC, and TA for those sites (Figure 3 a, b, c, d). These minima at GSO and GB coincided with heavy and persistent rains that led to record-breaking levels of peak river discharge and water levels at many long-term U.S.G.S stream gages (Zarriello et al. 2013). The largest salinity, DIC, and TA ranges in our PC data

Comparison of Measurement Error to Observations
The total relative errors for TA, DIC, and salinity at 1 standard deviation are 1.8%, 1.4%, and 1.2% respectively (Table 1). The calculated error range for pHc, determined from the combined error of TA, DIC, and salinity measurements is less than the observed daily range ( Figure 5). The offsets between pHc, pHe and pH EE shown in Figures 6, 7, and 8 are not due to error in TA, DIC, salinity, and in-situ temperature measurements, because the calculated error contribution is small (<.05, Figure 5). Additionally, Huang and Cai (2012)

Comparison of pHc to pH Electrode Measurement
At all sites, pHc, pH EE and pHe rise or fall similarly over a 24-hour sampling period (Figures 6,7,and 8). That is, variations are similar while absolute values are parallel but offset. For most observations, the offset between pHc and pHe or pH EE falls between -.5 and .5 (Figure 9). For GB, the offset between pHc to pHe and pH EE is not constant over time of the study ( Figure 6). pHc agrees well or is larger than pH EE at PC except for sample numbers 200 to 222 (which corresponded to March 9 th 2011) ( Figure 7). For that day, pHc steadily rose while pH EE remained at pH ~9 during the same period. There is agreement between pHc and pHe at GSO, except for offsets from sample numbers 0 to 50 and 283 to 300 (Figure 8). Between pHc and pH EE at GSO, the offset is not constant from 2010 to 2011.

Determination of Conservative Mixing Model End-members
The salinity, alkalinity, and DIC of the end-members are of key importance for determining the output of the model.  and has high salinity (35 gkg -1 ). We determined TA and DIC for this anomalous water using the same method that we used to determine the ocean end-member.
Comparing Model Results to pH Calculated from DIC and TA Figure 10 shows how pH can vary due to the mixing of river and ocean endmembers with two different modeling assumptions for the conservation of DIC: 1) DIC is conserved. pH mix is the pH from the mixture of river and ocean endmembers. The pH mix lines in Figure 10 show how pH mix increases due to increasing salinity, as shown by f o approaching 1, and decreasing temperature. The pH mix at 5 o C is higher than pH mix at 25 o C.
2) DIC is not conserved. A state of equilibrium is when the DIC flux is equal to zero; there is no dissolution of CO 2 into the estuarine water, nor does it evade out of it. We calculated pH equil , the pH at this equilibrium state, from the concentration of atmospheric CO 2 and the in-situ TA, salinity, and temperature measurements. pH equil shows the final pH a measurement if its DIC were to equilibrate with the atmosphere.
Since the carbonate system inhibits the degassing or evasion of CO 2 compared to a non-reactive gas, the pH of a river and ocean water mixture, pH mix , may not necessarily be at equilibrium and equal pH eqiul . However, pH equil and pH m increase linearly with increasing salinity (Figure 10). While pH equil varies due to temperature and possibly seasonal variations in alkalinity, its range is clearly less than of pHc ( Figure 11), which was determined from in-situ TA, DIC, temperature, and salinity.
The zone of stability, a segment where pH doesn't sharply decrease with salinity is between 0.5 and 1 f o because high salinity is accompanied by high alkalinity. The pHc of GSO are grouped together at the upper pH range; the outliers are connected to the great flood of 2010 ( Figure 11). PC has a larger pH range than GSO and has points of the same temperature that exceed pH mix . GB has a larger pHc range than PC and GSO. At all sites the variation of pHc exceeds that of pH mix and pH equil .

Explanation for pH Electrode Differences
The specific electrodes used to make the pH measurements may contribute to the offsets of pHc, pHe, and pH EE . Individual electrodes identified with unique ID numbers used to measure pH EE at PC tend to have a positive offset (pHc>pH EE ), a negative offset (pHc<pH EE ), or an offset centered at 0 (pHc~pH EE ). The time from calibration did not appear to have an influence on the magnitude of the offsets. In this simple case, since the offsets are constant within the sample period one may simply apply a correction factor to an electrode with a previously mentioned defect.

What Controls Short-Term pH Change in an Estuary?
Temperature varied seasonally (0.8 to 26.4 o C), but not significantly over individual 24-hour periods, which is generally within a range of 5 o C (Figure 4 and Temperature is not a significant control of pH equil because nearly all of the samples in Figure 10 fall within the pH equil range of 7.9 to 8.1. Since pH equil is a function of alkalinity and DIC at equilibrium, the narrow span of pH equil can also be attributed to changes in alkalinity. A span of pH equil at one f o value can be due to seasonal variability in the ocean and river end-members, or non-conservative sinks and/or sources of alkalinity. However, this range is considerably smaller than the ranges of pHc shown in Figure 11. Sulfate reduction and denitrification, which generate alkalinity, are active in Narragansett Bay sediment (Elderfield et al. 1981, Gains and Pilson 1972, Sampu and Oviatt 1991, Berousky and Nixon 1983. However, reoxidation of reduced S, and Fe decreases alkalinity. If these sedimentary processes (sulfate reduction, and oxidation of reduced species) are in balance; the net impact on alkalinity is zero (Kling et al. 1991). These non-conservative influences might conceivably affect pH seasonally, but they cannot drive pH variation in the water column on hourly time-scales.
Non-conservative alkalinity (TA generation or reduction) does not affect pH in the short term as evidenced by the narrow range of pH equil (Figure 10). The range in 24-hour pH change does not appear to be driven by changes in TA because pH equil follows the curvature of the pH mixing line (Figure 10) and if non-conservative alkalinity processes occur on a short-time scale, pH equil would have a large range at given temperature and f o . Figure 12 shows the daily difference between the 24-hour DIC range and the 24-hour TA range of a site. Positive values indicate DIC had a higher daily range than TA, and vice versa. DIC generally has a higher daily range than TA. Since we have already explained why temperature and TA are not the principal cause of observed pH changes within a 24-hour period, the only variable that remains to drive pHc variation is DIC.

Net Heterotrophy and Autotrophy Explained by Excess and Deficit DO and CO 2
The departure of dissolved O 2 or CO 2 from equilibrium can be driven by biology. The fractional departure from equilibrium for DO and CO 2 from Williams and Follows (2011) where CO 2 * is dissolved and hydrated CO 2 . The fractional departure from equilibrium of carbon dioxide is positive when there is excess CO 2 . As a result, the pH measured is below the pH of the water if it were at equilibrium with the atmosphere ( Figure 13). Atmospheric gas exchange can erode the biological imprint. While in our data, the correlation between excess CO 2 * and DO is not as strong as its relationship to pH below or above equilibrium (Figure 14), the general trends of the fractional departure of CO 2 * and DO are anti-correlated (Figures 15).
pH disequilibrium due to excess or deficit carbon dioxide and the fractional disequilibrium of DO are correlated (Figures 16 , 17). The fractional disequilibrium of DO (‗biological' signal left as DO) is less than the fractional disequilibrium of CO 2 because, excess DO is more efficiently eroded by gas exchange than excess CO 2 due to the buffering of the carbonate system.  (Dawicki 2010). An important factor to consider when comparing these two periods is that the water residence time of the estuary was probably much shorter during April 2010 than April 2011 because of the extreme flooding. One episode when high chlorophyll concentrations correlated with a large CO 2 * deficit was during the winterspring bloom of 2011 (the last 50 sample numbers). This finding highlights two important points: (1) pH change due to photosynthesis doesn't necessarily occur instantaneously because time must pass for the ‗biological signal' to accumulate, and (2) mixing and gas exchange can erode a biological pH perturbation.

The Role of Mixing Efficiency on Short-term pH change
While biological processes influence pH, physical processes such as water residence time and gas exchange influence the extent to which the biological ‗signal' will accumulate. The efficiency at which gas exchange erodes a deficit or excess is determined by the gas exchange timescale (Williams and Follows 2011). By comparing the exchange timescale to the timescales of other estuarine processes, such as the length of a tidal cycle or water residence time, we can further our understanding of hourly and seasonal pH variations.
The timescale to equilibrium for a non-reactive gas such as DO is where T is the equilibration timescale of DO (days), h is the water depth of the site (m) , and K g (ms -1 ) is the coefficient of gas exchange which is a function of windspeed and water turbulence. In contrast, the timescale for CO 2 equilibrium is where B is the Revelle Buffer Factor. In this work we refer to T and T c as the mixing efficiency of DO and CO 2 respectively.
While wind speed is typically the principal parameter used to estimate the gasexchange coefficient (e.g., Roques 1985, Raymond and Cole 2001, Ho et al. 2014, Wanninkof (1992), turbulence due to tidal currents in estuaries when wind speed is below 5 ms -1 can be more important than the wind in controlling gas exchange coefficients (Borges et al. 2004, Raymond andCole 2001. The coefficient of gas exchange due to wind and flow is K g = K g,wind + K g , flow (12) (Borges et al. 2004). While Roques (1985)  We use the parameterization given by Wanninkof (1992) for K g because it contains a formulation for both DO and CO 2 based on the wind speed and physical properties of the water. We used hourly mean wind speeds from Quonset Point and matched them with each sample (National Oceanic and Atmospheric Administration (2013)).
We calculate the water residence time to compare it to the gas exchange mixing efficiency (h/Kg) of the bay. We estimate the monthly average freshwater discharge (Q m ) by adding the monthly average discharge within the period of the study of Blackstone, Pawtuxet, and Taunton rivers obtained from the USGS hydrology database. The monthly average residence time was determined using Q m and the relation by Pilson (1985), who derived a relation between the residence time and freshwater input using the following empirical relation: DO equilibrates much more quickly than CO 2 ( Figure 19). On average, the equilibrium timescales of DO and CO 2 are 9 and 155 days, respectively (the standard deviation is 7 and 155 days). If the wind speed is less than 5 ms -1 , the time scale to equilibrium of CO 2 due to tidal and non-tidal currents is at least 70 days (much greater than the residence time of the bay Using a conservative mixing model, we have shown that pH variation at the three studied sites is mainly due to differences in DIC driven by photosynthesis and respiration, rather than simply changes in TA and DIC from mixing of different proportions of ocean and river water. Excess carbon dioxide correlates with deficit dissolved oxygen and vice-versa, indicating that DIC varies seasonally due to respiration and photosynthesis. However, the relation between excess and deficit carbon dioxide is not clearly linked to chlorophyll concentration. The relationship of DO to DIC is complicated by the differences in gas exchange rates of O 2 and CO 2 . Analysis of the gas exchange mixing efficiency of the estuary provides a physical explanation as to why pH values below equilibrium CO 2 covary with low DO concentrations.   Figure 1. Sampling sites at Narragansett Bay, Rhode Island.   Bottom: pH determined from alkalinity, total dissolved inorganic carbon, salinity, and in situ temperature measurements (pHc). Figure 5. Range of relative error (rer) of pHc calculated from chemical measurements (shown filled) compared to the observed daily range in pHc (shown empty). Figure 6.A) pH calculated from chemical measurements (pHc) compared to pH measured by our electrodes (pHe) at Greenwich Bay, over sample number. B) calculated pH (pHc) compared to pH measured by RIDEM's electrodes (pH EE ) at Greenwich Bay, over sample number. Figure 7. A) pH calculated from chemical measurements (pHc) compared to pH measured by our electrodes (pHe) at Potter Cove, over sample number. B) calculated pH (pHc) compared to pH measured by NBNERR's electrodes (pH EE ) at Potter Cove, over sample number. Figure 8. A) calculated pH (pHc) compared to our pH measured by our electrodes (pHe) at GSO over sample number. B) calculated pH (pHc) compared to pH measured by RIDEM's electrodes (pH EE ) at GSO over sample number. Figure 9. A) The pH measurements from the electrodes (with pH EE measured by the external electrodes and pHe measured by our electrodes) compared to calculated pH (pHc), with calculated pH in the X axis. B) The pH measurements from the electrodes compared to calculated pH (pHc) over time. Figure 10. A) pH mix compared to pHeq (pH if DIC was at equilibrium with the atmosphere) at Greenwich Bay . B) pH mix compared to pHeq at Potter Cove, C) pH mix compared to pHeq at GSO. pH mix Figure 11. pH(TA,DIC) denotes pH calculated, also referred as pHc. A) pH mix compared to pHc at Greenwich Bay. B) pH mix compared to pHc at Potter Cove. C) pH mix compared to pHc at GSO. pH mix Figure 12. Magnitude of daily DIC range relative to daily TA range. Figure 13. The fractional departure from equilibrium of carbon dioxide (dCO 2 * /CO 2 * ) and its relationship to pH (the difference between pH calculated from TA and DIC and pH when DIC is at equilibrium to the atmosphere (pH m -pH eq)).      Figure 19. The timescales of carbon dioxide equilibration and dissolved oxygen equilibration compared to the flushing time of the bay. The flushing time of the bay was calculated from river discharge and a relation of freshwater input to flushing time (Pilson 1984).

FIGURES
Only at GB did the largest daily range in Ωc and Ωa coincide with the largest daily range in salinity. It is clear that for Narragansett Bay, the factors that control pHc, the Revelle Factor, and Ωc and Ωa are more complex than dilution of TA and DIC by precipitation or freshwater discharge.                                               ) and the relationship to pH (the difference between pH calculated from TA and DIC and pH when DIC is at equilibrium to the atmosphere (pH m -pH eq)).       (Kaushal et al. 2013), alkalization of the Branch River has been statistically insignificant (Kaushal et al. 2013 Supporting Information). Blackstone River alkalinity is increasing at a rate of ~0.16 mgL -1 yr -1 . Since the most recent data is from 2001, the TA of the river end-member may be underestimated (by ~30 µmolkg -1 ); The salinity of the measurements are reported by the USGS as conductivity; all values below the detection limit. DIC is not measured by the USGS. We determined the DIC end member from TAc and the average pH obtained from the USGS of rivers mentioned earlier.
The end-members determined in this study are similar to those found by  for TA and DIC of the Blackstone, Runnins, and Palmer Rivers. While Boucher (1991) attributed high pH to high alkalinity resulting from fertilizer runoff at the Taunton River,  found nitrate to be a minor component of alkalinity  (Cai et al. 2010). Their procedure was similar to the procedure that we used for this study, except their samples were not poisoned with mercuric chloride.

What contributes to error?
The offsets between pHc, pHe and pH EE are probably not due to error in TA, DIC, salinity, and in-situ temperature measurements, because the calculated error contribution is too small (<.05, Figure 19). Additionally, Huang and Cai (2012) found that TA and DIC samples can be stored with minimal error if they are in borosilicate glass (for TA) and high density polyethylene (HDPE) bottles (DIC); samples can be stored in the dark for a period of at least 3 months. Thus, the differences between these independent pH estimates is likely due to errors associated with the electrodes.
Various factors can contribute to electrode errors, such as a dramatic changes in pH or salinity, the type of buffer used to calibrate the electrode, or the protocol used to handle or correct the data.
In this study, rapid changes in temperature or salinity do not appear to have significant affected offsets between the electrodes. Calculated instance on April 2010 GSO and GB experienced a dramatic change in salinity in the course of 24 hours but the offset between pHc and the pH measured by electrodes was not different from other days (Figure 9 in Figures). For subsequent sampling intervals, the electrodes were calibrated with certified NBS buffers. The pH calculated using seawater scale is .159 less than pH calculated using the NBS scale . While the pH meter did not have different calibration points (pH=7,10) when using different buffers, the offset at the beginning of the sample sequence at all sites is at a similar range (~0.2), and may partly be due to this calculation difference. The offset between pHc and pHe is negative (pHc < pHe) for the last 50 to 100 measurements, but it cannot be explained by using an NBS buffer. pH EE is not offset like pHe for the last measurements and is less clear; it is either less than (GSO, GB) or equal to (PC) pHc.
The specific electrode used to make the pH measurements may contribute to the offset. The same electrodes identified with unique ID numbers used to measure pH EE at PC tend to have a positive offset (pHc>pH EE ), a negative offset (pHc<pH EE ), or an offset centered at 0 (pHc~pH EE ) (electrode ID numbers and sonde dates from Daisy Durant, personal communication). The time from calibration did not appear to have an influence on the span of the offset. In this simple case, since the offsets are constant within the sample period one may simply apply a correction factor to an electrode with a previously mentioned defect.
Alkalinity distribution in the western North Atlantic margins. Journal of Geophysical Research: Oceans (1978-2012