Estuaries are the nexus between terrestrial and oceanic aquatic systems, and the sites of some of the heaviest population densities in the world (Nixon 1995). Estuaries also provide important ecosystem services such as nursery and fishery habitats, filtering and detoxification, and flooding and storm event mitigation (Barbier et al. 2011). However, estuaries are threatened by changing atmospheric conditions (nitrogen deposition, carbon dioxide enrichment), oceanic environmental change (ocean acidification, sea level rise, warming, frequency and intensity of storms), and changes in terrestrially derived inputs (eutrophication, organic matter fluxes, increased runoff ).

The cumulative impacts of these changes on estuaries are unclear. On one hand, estuaries are commonly heterotrophic, high CO 2 environments that are more susceptible to acidification than adjacent ocean waters (Cai et al. 2011). The primary sources of acid buffering in ocean water have long been known to be inorganic (e.g., modulated by dissolved carbonate [CO 3 2À ] and bicarbonate [HCO 3 À ] ions; Park 1960), but the contributions of these ions to buffering in estuaries are commonly lower (Hu and Cai 2013). The carbonate/bicarbonate buffer regulates pH and the partial pressure of carbon dioxide (pCO 2 ) by H + exchange equilibria:

While CO 3 2À and HCO 3 À ions are the primary contributors to total alkalinity (TA) and pH buffering, other charged species can make significant contributions as well. Organic alkalinity (OrgAlk) has been identified as an important contributor to TA in riverine and low-salinity coastal environments (Hudson-Heck & Byrne 2022; Waldbusser and Salisbury 2014) including Gulf of Maine rivers (Hunt et al. 2011), the Kennebec estuary (ME, USA, Hunt et al. 2013), intertidal salt marshes (Song et al. 2020), some southeastern US estuaries (Cai et al. 1998), Baltic Sea estuary waters (Kuli nski et al. 2014), Gulf of Mexico estuaries and coastal waters (Yang et al. 2015), and Korean coastal waters (Ko et al. 2016). The term organic alkalinity refers to the contributions of weak organic acids to TA-a contribution that can be modeled in terms of the total concentrations of conjugate organic acids/bases, relevant acid dissociation constants (pK a ), and in situ pH. The contributions of a particular organic acid to TA may be quite different in acidic and alkaline estuaries because the contributions of organic bases to OrgAlk are pH dependent. While organics constitute potentially important alkalinity components, the overall sources and roles of organic acids in driving physiochemical reactions within estuaries remain unclear. Without a better understanding of the interplay between organic and inorganic alkalinity in estuaries and their coastal plumes, the potential of estuaries to respond to acidification threats from both land and sea cannot be determined.

Examinations of aquatic carbonate systems can utilize measurements of TA, pH, dissolved inorganic carbon (DIC), and the partial pressure of carbon dioxide (pCO 2 ). Measurements of two of these parameters, together with appropriate pK a values are commonly used to model pH buffering behavior in lakes (Cole et al. 1994;McDonald et al. 2013), rivers (Butman and Raymond 2011;Raymond et al. 2013), estuaries (Borges 2005), and ocean waters (Park 1960). Software packages such as CO2SYS (Lewis and Wallace 1998) and SeaCARB (Gattuso et al. 2021) are available across a wide range of computing platforms to facilitate these calculations. However, if TA is used as one of the inputs for these calculations, and OrgAlk is present in significant quantities, then derived results will be inaccurate (systematically biased). For example, if TA and pH are used to derive pCO 2 and DIC, and OrgAlk is significant, DIC and pCO 2 may both be substantially overestimated (Abril et al. 2014). Recent estimates of CO 2 release from US lakes (McDonald et al. 2013), US rivers (Butman and Raymond 2011), and global rivers (Raymond et al. 2013) modeled CO 2 fluxes from the combination of TA and pH; consequently, our understanding of global terrestrial and estuary CO 2 fluxes is subject to large potential uncertainties due to the effects of OrgAlk.

Estimating the contribution of a charge group to TA requires knowledge of both the concentration of that group and its dissociation constant. The pK a values of carbonate and bicarbonate are characterized and predictable from salinity, temperature and pressure. The pK a values of OrgAlk, although influenced by salinity, temperature, and pressure, are not well understood. Studies that have characterized the pK a of estuary OrgAlk have yielded a continuum of values from less than 4.5 to greater than 7.5, indicating that OrgAlk acid-base chemistry is complex (e.g., Cai et al. 1998;Kuli nski et al. 2014;Yang et al. 2015;Ko et al. 2016;Song et al. 2020;Kerr et al. 2023a,b;Song et al. 2023).

In studies of seawater (Dickson 1981) and freshwater (Stumm and Morgan 1995;Drever 1997), TA is discussed as the sum of anions in solution which can be neutralized by strong acid. In both aquatic environments, the pH "equivalence point" has been operationally set at pH 4.5. The definition from Dickson (1981) is presented in Eq. 2, where any species with a pK a greater than or equal to 4.5 at zero ionic strength is defined as a base (or proton acceptor) while any species with a pK a less than 4.5 is defined as an acid (or proton donor). This definition has served the oceanographic community well, as the inorganic components of seawater TA contribute negligibly to TA near pH 4.5. Current seawater analysis methods call for titration at lower pH (3.5-3.0; Dickson et al. 2007). However, with accurate pH measurements, TA can be measured at higher pH, providing results consistent with the formal definition of TA (Liu et al. 2011).

However, definitions of TA have included a catch-all term of unspecified organic anions (OrgAlk À terms in Eq. 2, denoted simply as OrgAlk in this work). These organics will contribute to TA in a manner consistent with Eq. 2, provided that they become fully protonated at or above pH 4.5 (i.e., have a pK a substantially greater than 4.5, termed [OrgAlk À pKa≥4.5 ] in Eq. 2). However, there is increasing evidence that the acidbase behavior of naturally occurring organic anions is inconsistent with this convention, with some functional groups having a pK a near or below 4.5 ([OrgAlk À pKa<4.5 ] in Eq. 2; Ulfsbo et al. 2015;Sharp and Byrne 2020;Song et al. 2020;Sharp and Byrne 2021;Kerr et al. 2023a).

In this study we sampled two Gulf of Maine estuary systems: the Pleasant estuary in Maine, USA, and the St. John estuary in New Brunswick, CA. Samples were collected along the estuary salinity gradient and at the river endmember over four spring and fall transits. Using two different measurement protocols, these samples were analyzed via titration with base for several parameters including OrgAlk charge group concentrations and pK a . This work presents the resulting OrgAlk concentrations, modeled estuary organic matter pK a values and charge group concentrations and examines retrievals of pH using inorganic carbon system calculations.

Based on previous work documenting contrasting levels of dissolved organic carbon (DOC), TA, OrgAlk, and pH measured at several New England and Canadian river endmembers (Hunt et al. 2011), two river-estuary systems were selected for this study (Fig. 1). The Pleasant river drains an approximately 160 km 2 watershed forested in deciduous trees, but is also characterized by large regions of heath predominantly used to cultivate wild blueberries. Pleasant river water is known to be rich in tannins (a synonym for humic acids), and the darkly colored water empties into the marshfringed estuary at the town of Columbia Falls (Keller 2020). The St. John river drains a much larger watershed, approximately 55,000 km 2 , which encompasses areas of Maine (USA) and New Brunswick (Canada). The river empties into the Bay of Fundy at St. John, New Brunswick, although vigorous tidal mixing occurs above and below this location. The watershed is mostly forested, with occasional agricultural areas. Soils are loamy and well-drained, overlying a mixture of limestone and sandstone bedrock (Fahmy et al. 2010).

In order to assess potential differences in estuary conditions between spring and fall seasons, four surveys of the Pleasant and St. John estuaries were conducted in May and October of both 2018 and 2019. Estuary samples were collected during single-day surveys on small vessels in each system, departing from Addison Maine for Pleasant estuary surveys and from St. John, New Brunswick, for St. John surveys. Estuary water was continuously pumped to an underway measurement system, which recorded location, salinity, water temperature, and the partial pressure of carbon dioxide (pCO 2 ) among other parameters. A detailed description of this underway system can be found in Hunt et al. (2013). Surveys began on the incoming tide and lasted through high tide and into the ebb tide. At intervals determined from the underway salinity, surface water was captured for discrete sample collection. During the October 2017 and May 2018 surveys a Niskin bottle was lowered overboard by hand; during the later surveys a 10-L high-density polyethylene carboy was rinsed and filled from the outflow of the underway system, then tightly capped until samples were drawn from a spout at the bottom of the carboy. River endmember samples were collected from above the final downstream dam on each river. For the Pleasant, this dam formed a physical tidal barrier, and the transition from river to estuary was immediate. For the St. John the closest site was in Fredericton New Brunswick, a location over 120 km from the estuary mouth along the river's course. For both endmember sites, a plastic bucket was lowered from the center of a bridge over the river, rinsed three times with river water, and samples were collected as described earlier. The temperature and conductivity of samples were measured directly from the bucket with a handheld meter (YSI).

Water from the Niskin or carboy was transferred without bubbling into individual, previously-flushed borosilicate glass bottles: 500 mL for alkalinity and pH analyses, and 300 mL for inorganic carbon (DIC) analysis. All bottles had greased stoppers and positive closure mechanisms. All were filled to leave less than 1% headspace in the bottle and were preserved with saturated mercuric chloride solution. Samples for silicate and phosphate analysis were filtered using a plastic syringe and 0.2 μm cartridge filter into acid-washed and previously rinsed 50-mL high-density polyethylene vials and preserved with chloroform. Samples for DOC were filtered as was done for the nutrients into acid-washed, previously rinsed 30-mL high-density polyethylene bottles. All samples were immediately placed on ice. Alkalinity, pH (on the total pH scale, pH T ), and DIC samples were refrigerated until analysis; nutrient and DOC samples were frozen until analysis.

Discrete sample salinity was measured with a Guildline Portasal salinometer (Guildline, Smiths Falls Canada). The pH T of samples above pH T 7.0 was measured spectrophotometrically with meta-cresol purple (mCP) using 10 cm pathlength cylindrical glass cells and an Agilent Technologies Cary 8454 UV-Vis spectrometer (estimated pH T precision: 0.001). Samples measured using mCP ranged in salinity from 0.5 to 32.5 (Douglas and Byrne 2017). The same instrument was used to verify the response slope of a combination glass pH electrode (Metrohm EcoTrode Plus), as described in Supporting Information Section S1. For sample pH T less than 7.0, and therefore outside the working range of mCP, the initial electrode mV reading and zero-pH T intercept potential (E 0 ) determined from the initial TA titration (Alk Gran1 , equivalent to TA, see Alkalinity titrations section; Easley and Byrne 2012) were used to calculate the pH T of the untitrated sample. All pH T measurements were performed on samples preserved with mercuric chloride. The DOC was measured with an uncertainty of 1.5 μmol kg À1 using a Shimadzu high temperature catalytic oxidation analyzer with chemiluminescent detection. Nutrients including phosphate and silicate were analyzed using a SmartChem automated analyzer (Westco Scientific) according to standard colorimetric methods. The resulting measurement uncertainties were 0.8 and 0.25 μmol kg À1 , respectively (Strickland and Parsons 1972). The DIC was measured by acidifying each sample in a custom-built gas extraction system and measuring the evolved CO 2 with a Picarro G5131-I cavity ringdown spectrometer (Picarro), with an estimated measurement uncertainty of 2 μmol kg À1 .

The TA and OrgAlk titrations were conducted using a custom-built apparatus similar to that presented in Cai et al. (1998). This system performed several successive titrations on the same water sample. The TA of each sample was measured by Gran titration (Alk Gran1 ) according to an accepted method ("Standard Operating Procedure 3b"; Dickson et al. 2007), followed by measurement of the carbonate-free alkalinity also using the Gran titration approach (NC-Alk Gran2 ), and finally the carbonate-free alkalinity was measured according to an endpoint approach at pH T 4.5 (NC-Alk 4.5 ). Details of the analyses are provided in Supporting Information Section S2. Briefly, each sample was initially titrated from the initial pH T (pH Ti ) to a pH T of 3.5, bubbled with nitrogen, then titrated to pH T 3.0 (Alk Gran1 ). CO 2 -free NaOH (described in Supporting Information Section S3) was then added to return the sample to an alkaline pH i . The sample was then titrated to pH T 3.0 (NC-Alk Gran2 ). This process was then repeated, with the final titration ending at pH T 4.5 (NC-Alk 4.5 ). Repeated analyses of certified reference material (CRM; Dickson et al. 2003) produced a mean deviation from CRM alkalinity of À2.1 μmol kg À1 with a standard deviation of AE 5.0 μmol kg À1 .

We generally followed the methods presented by Cai et al. (1998), Song et al. (2020), and Kerr et al. (2023a) to estimate both organic proton binding site concentrations (XT i ) and corresponding acid dissociation constants (pK ai ). Details are provided in Supporting Information Section S4. Briefly, a sample was acidified to pH T 3.0 via Gran titration (Alk Gran1 ), then automatically titrated stepwise under nitrogen with small additions of CO 2 -free NaOH from pH T 3.0 to pH T 8.5 or 10, resulting in several hundred sequential NaOH additions.

Calculation of Alk Gran1 , NC-Alk Gran2 , and NC-Alk 4.5

Alk Gran1 and NC-Alk Gran2 were calculated using the Gran function (Gran 1952) that included a nonlinear least squares correction for the presence of sulfate and fluoride ions (Dickson et al. 2007). At an endpoint of 4.5, NC-Alk 4.5 was simply determined as the difference between the concentration of added protons from the HCl titrant and the measured proton concentration:

where m A is the mass of added HCl titrant, c A is the concentration of HCl titrant, m 0 is the initial sample mass, and [H + ] is the proton concentration determined from the endpoint pH T measurement. The titration pH T was calculated from the observed E 0 determined during the Alk Gran1 measurement for each sample:

where E is the electrode potential (volts) measured at the titration endpoint, E 0 is the electrode intercept potential, R is the gas constant (8.3145 J K À1 mol À1 ), T is the Kelvin temperature of the titration, and F is the Faraday constant (96,487 C mol À1 ).

As NC-Alk Gran2 and NC-Alk 4.5 titrations were performed under CO 2 -free solutions, their values are represented as the sum contribution of non-carbonate alkalinity components (NC-Alk x ):

where NC-Alk x is either NC-Alk Gran2 or NC-Alk 4.5 . OrgAlk x represents the contribution of organic species to NC-Alk Gran2 or NC-Alk 4.5 . It was calculated as the residual after all other alkalinity species were taken into account. Phosphate and silicate CRM concentrations were both taken from reported CRM documentation. For natural samples they were measured by standard colorimetric methods using a SmartChem automated analyzer (Westco Scientific).

Nonlinear least squares fitting of the NaOH titration curve produced estimates of both XT i (the concentration of organic proton binding group i) and pK i (the acid dissociation constant of organic proton binding group i). Details of this analysis are provided in the Supporting Information. Briefly, this approach is identical to that of Cai et al. (1998), Song et al. (2020), and Kerr et al. (2023a), with the exceptions that (1) terms used by Song et al. (2020) and Kerr et al. (2023a) to account for excess CO 2 in the NaOH titrant were excluded, and (2) we modeled both the entire NaOH titration curve as was done in other studies, and also subsets of the NaOH titration curve over a more limited range of pH T .

The quantities of OrgAlk Gran2 and P XT i are not directly comparable, as OrgAlk Gran2 only represents the organic anions that are unprotonated at pH i (i.e., [Org À ]), while P XT i represents the sum concentrations of i organic charge groups in solution (i.e.,

). To account for this difference, we followed the approach of Song et al. (2020), which uses the OrgAlk measured from pH i (OrgAlk Gran2 ) together with the component fractions of XT i comprising P XT i and the dissociation constants (K i ) provided by the NaOH titration, to calculate the total organic proton binding group concentration XT Gran2 :

where [H þ i ] is the hydrogen ion concentration at pH i , which is the pH T at which OrgAlk Gran2 was measured.

To evaluate the influence of OrgAlk on estuary water chemistry, we chose to examine differences between observed pH T and those calculated from several combinations of carbonate system parameters (Alk Gran1 , DIC, pCO 2 ). We used a modified version of CO2SYS (Van Heuven et al. 2017) provided by Song et al. (2023), which accepts the input of the pK ai and charge group concentrations (XT i ) of three OrgAlk groups, together with silicate and phosphate concentrations. The inorganic carbon K 1 and K 2 constants chosen were those of Millero et al. (2010), the K SO4 and K B constants were those of Dickson et al. 1990 andDickson 1990, respectively, and the total boron concentration was calculated from salinity according to Uppström (1974). A discussion of uncertainty propagation in the pH T calculations and potential sources of interference is presented in Supporting Information Sections S6 and S7.

The Pleasant endmember was highly acidic and poorly buffered, with a mean pH T of 4.40 and mean Alk Gran1 of À 39 μmol kg À1 (Table 1). The negative alkalinity concentration relates to a deficit of proton donors relative to proton acceptors; as the equivalence point of TA is defined at pH T 4.5 (Dickson 1981) a sample with a natural pH T less than 4.5 is expected to exhibit negative Alk Gran1 . The St. John was more buffered, with a mean pH T of 6.81 and mean Alk Gran1 of 650 μmol kg À1 . The mean Pleasant endmember DOC (1238 μmol kg À1 ) was also double that of the St. John (612 μmol kg À1 ), while the mean St. John DIC was more than four times higher than that of the Pleasant. The October surveys in both systems followed dry summers with low river discharge and coincided with the highest endmember pH T and Alk Gran1 , DIC, and DOC concentrations.

Alk Gran1 , pH T , and DOC distributions with salinity in both the Pleasant and St. John reflected the mixing of the distinct river endmembers with a common Gulf of Maine higher-salinity endmember (Fig. 2). Alk Gran1 and pH T in the Pleasant estuary were consistently lower than the St. John at the same salinity. Alk Gran1 in both estuaries reflected mostly conservative mixing across the salinity gradient. However, at salinities less than 3 the Pleasant estuary Alk Gran1 exhibited some nonlinear characteristics with lower-than-conservative Alk Gran1 .

As pH T quantifies proton concentrations on a logarithmic scale, nonlinear pH T distributions with salinity are expected. Although pH T values below 6 in the Pleasant estuary reflected a strongly acidic system, pH T was higher by several tenths across the salinity range during May surveys in the Pleasant estuary when compared to October surveys, especially in midrange salinities from 3 to 25. The opposite was true in the St. John estuary, when salinity was lower in May than October. In contrast to Alk Gran1 and pH, DOC was consistently higher in the Pleasant estuary than in the St John at a comparable salinity and season. While St. John DOC-salinity distributions were similar across the four surveys, with the possible exception of the October 2019 St. John survey, DOC concentrations across the Pleasant estuary salinity gradient in October were more than twice as high as those in May (Fig. 2).

Organic alkalinity, measured as OrgAlk Gran2 and OrgAlk 4.5 , was observed in both the Pleasant and St. John estuaries in all four surveys (Fig. 3, Table 1). As with Alk Gran1 , the Pleasant endmember OrgAlk Gran2 was consistently negative, reflecting the low pH T conditions of the Pleasant River. This low pH T did not permit the measurement of OrgAlk 4.5 . The St. John low-salinity endmember had consistent OrgAlk Gran2 and OrgAlk 4.5 concentrations, with mean values of 43 AE 5.6 and 28 AE 3.8 μmol kg À1 , respectively. Estuarine mixing rapidly changed the distributions of OrgAlk Gran2 and OrgAlk 4.5 in the Pleasant estuary, with increasing salinity coinciding with OrgAlk Gran2 and OrgAlk 4.5 increasing to mid-estuary maxima and then decreasing towards the ocean endmember. This lowsalinity increase was particularly large in the Pleasant October surveys, when OrgAlk Gran2 rose more than 100 μmol kg À1 . OrgAlk Gran2 and OrgAlk 4.5 were typically higher in the Pleasant estuary than in the St. John above a salinity of 3 in the October surveys, while concentrations were similar between the two systems during the May surveys. Maximum OrgAlk Gran2 and OrgAlk 4.5 concentrations were typically found between salinities 1-11, with exceptions in the Pleasant estuary in May 2018 where the maximum values were at higher salinities, and the St. John in October 2018 when the maximum OrgAlk 4.5 was found at the highest salinity (32.10). OrgAlk Gran2 concentrations were consistently higher than the respective OrgAlk 4.5 concentrations at low and middle estuary salinity, but the concentrations typically became comparable at salinities above 25. OrgAlk can also be estimated as the difference between titrated TA and TA calculated from other carbonate system parameters (e.g., pCO 2 and DIC; Hunt et al. 2011;Ko et al. 2016;Song et al. 2020). However, a comparison of Pleasant and St. John estuary titrated OrgAlk Gran2 results to OrgAlk calculated according to this difference approach (using pCO 2 and DIC to estimate TA) found no correspondence (p > 0.08, r 2 = 0.04, data not shown). Song et al. (2020) also found no correlation between these two OrgAlk measures.

Whole-pH titration results ( P XT i , pK a ) Modeling of the NaOH titration data resulted in consistent pK a values for OrgAlk (Table 2). Three organic proton binding groups were returned by the model when all titration data were used, with overall mean pK a values of 4.16 (AE 0.35), 5.93 (AE 0.50), and 8.49 (AE 0.21). While the discussion focuses on these results, it is worth noting that modeling NaOH titration data between pH T 3.0 and sample in situ (pH i ) produced either two or three groups, indicating that the pH T range of data modeled impacted the model output. There was no statistical difference between mean pK a in the Pleasant and St. John estuaries, and there were no seasonal differences between May and October pK a for either estuary.

Analysis of NaOH titration data also produced organic charge group concentrations (XT i ) for the three selected organic proton binding groups (see Supporting Information Section S4). Concentrations of XT 3 (mean pK a3 8.49) were always greatest, typically followed by XT 1 (mean pK a1 4.16), and XT 2 (mean pK a2 5.93). The total concentration of all organic charge groups ( P XT i = XT 1 + XT 2 + XT 3 ; Fig. 4) ranged from 158 μmol kg À1 in the highest-salinity Pleasant estuary sample in May 2019 to 1350 μmol kg À1 in the Pleasant estuary in Oct. 2018. The mean P XT i for all samples in both estuaries was 361 μmol kg À1 (AE 194 μmol kg À1 ). The proportional contribution of each group to P XT i was consistent: 21% AE 9% XT 1 (range: 1%-54%), 8% AE 5% XT 2 (range 0%-24%) and 71% AE 11% XT 3 (range 33%-93%).

XT Gran2 was almost always lower than respective P XT i (Fig. 4), and neither showed any trend with salinity. Note that negative values of OrgAlk Gran2 returned negative values of XT Gran2 according to Eq. 6. As a negative total concentration is not possible (unlike a negative alkalinity defined relative to a proton equivalence point), we have ignored these values in the following analysis. The mean XT Gran2 for all samples was 136 μmol kg À1 (AE 133 μmol kg À1 ), with a maximum and minimum of 510 and 16 μmol kg À1 , respectively. Overall, Pleasant estuary XT Gran2 was not statistically different from St. John estuary XT Gran2 (two-sample t-test, p = 0.36), and there were no seasonal differences ( p = 0.11).

Organic alkalinity was present in both the Pleasant and St. John endmembers and estuary samples during all surveys. Indeed, measurable concentrations of OrgAlk were present in CRM as well, confirming findings reported by Sharp and Byrne (2021). Those authors described a method similar to our OrgAlk 4.5 measurement, and CRM OrgAlk concentrations (10.5, 10.9, and 7.6 μmol kg À1 for Batches 172, 176, and 183, respectively, applying the boron : salinity ratio of Uppström 1974) comparable to the concentration we measured in Batch 185 (5.2 μmol kg À1 , applying the Uppström ratio). Details of the OrgAlk method evaluation and CRM results are presented in Supporting Information Section S3. The ubiquitous presence of OrgAlk in natural waters from terrestrial to marine systems requires an understanding of the concentrations and chemical nature of this material if TA measurements are to be accurately used in carbon system calculations (Sharp and Byrne 2020).

Concentrations of OrgAlk Gran2 and OrgAlk 4.5 in the Pleasant and St. John estuaries were comparable to those reported in other studies (Fig. 3, Table 3), although the negative OrgAlk Gran2 values in the Pleasant are the larger than previously reported. Pleasant estuary OrgAlk Gran2 levels and distributions with salinity during October surveys were similar to those reported for the Satilla estuary by Cai et al. (1998), whose analytical approach was used for the OrgAlk Gran2 measurements in this study and whose surveys of the Georgian estuary were also conducted in October. The Satilla zerosalinity endmember also had a very high DOC concentration 1998) was not as low as our Pleasant endmember observations, the Satilla pH did approach 5.5 (on the National Bureau of Standards-NBS-scale) at the endmember, the lowest level registered among the studies presented in Table 3.

The Altamaha estuary presented by Cai et al. (1998) most closely resembled the conditions we observed in the St. John, with comparable OrgAlk Gran2 (about 5-50 μmol kg À1 ), DOC concentrations (about 350-750 μmol kg À1 ), and pH and Alk Gran1 near the river endmember (about 6.6 on the NBS scale and 500 μmol kg À1 , respectively). The Alk Gran1 and pH at the Baltic sites of Kuli nski et al. ( 2014) were much higher than those in the St. John, with lower DOC concentrations as well. Overall, the Satilla estuary is the closest analogue to the Pleasant estuary, while the Altamaha is the closest analogue to the St. John estuary among the systems described in the literature.

The low-salinity region of estuary mixing is typically the site of dramatic pH increases, particularly in the acidic Pleasant system. Organic alkalinity mixing in the Pleasant estuary surveys also resulted in OrgAlk Gran2 and OrgAlk 4.5 peaks in the middle of the salinity gradient. Cai et al. (1998) documented similar mid-estuary OrgAlk maxima and attributed the phenomenon to two different processes: rapid pH change in early estuary mixing followed by conservative mixing of organic alkalinity between the peak and the coastal endmember. If charge groups with sufficiently low pK a are present in the organic material, the rapid pH increase results in those groups being increasingly deprotonated at ambient pH and thus available for titration with acid. Cai et al. (1998) theorized that this pH change is of more importance to estuary OrgAlk contributions than the potential dependence of organic pK a on ionic strength (i.e., salinity). Others have pointed out that salt marshes and mangroves may represent inputs of alkalinity to estuaries, presumably including organic components, independent of river and ocean endmembers (Sippo et al. 2016;Wang et al. 2016), and this could explain the mid-estuary maxima in our observations. Song et al. (2020) proposed a large intertidal salt marsh OrgAlk contribution, representing 36% of the total OrgAlk concentration, during a time of limited freshwater input. However, recent work by Hinckley (2021) provides a counterargument. Hinckley (2021) serially diluted Pleasant and St. John river water with CRM to artificially simulate the estuary mixing process. These dilutions and titrations effectively removed the low-salinity pH change noted by Cai et al. (1998), but still showed a mid-salinity peak of OrgAlk Gran2 and OrgAlk 4.5 . As the only changes among the dilutions were the ionic strength and OrgAlk concentration, the pK a dependence of organic charge sites on ionic strength may need to be re-evaluated, and may be more important than previously reported.

We measured OrgAlk using two different approaches: a Gran-style interpretation of titration data between pH T 3.5-3.0, and a separate endpoint titration to the TA equivalence pH T of 4.5. If no OrgAlk was present in solution, or if the organic charge groups had pK a values considerably higher than 4.5 or lower than 3.0 (and thus became totally protonated or remained deprotonated during both titration procedures, respectively) then the concentrations of OrgAlk Gran2 and OrgAlk 4.5 would in principle be equal. Alkalinity titrations to different endpoints can be conducted reproducibly, represent the "correct" alkalinity quantity at that particular pH, and provide different overall alkalinities. Our work shows that these differences can be substantial. Organic anions may have a pK a that impacts the titration alkalinity, but which would not affect buffering or the overall acid-base chemistry at typical estuarine or ocean in situ pH, and careful consider- ation is required when measuring OrgAlk and discussing its contribution to TA. Indeed, there does not currently appear to be a rigorous means of including OrgAlk in a quantitative summation of all contributions to alkalinity. While models that included additional charge groups did not appreciably improve modeled Org-Alk fits to our observations, this does not imply that the organic charge groups present in the Pleasant and St John estuaries are actually uniform in their properties. Instead, it is likely that the organic charge groups are polydisperse with a number of distinct pK a values, as described by Paxéus and Wedborg (1985) and Cai et al. (1998). The simple model and dataset conditions we employed, which only encompassed the natural pH conditions of the Pleasant and St. John estuaries, could not account for charge groups with very low pK a , such as the pK a 2.66 group that was listed by Paxéus and Wedborg (1985) as the most abundant organic charge group in their sample. A charge group with pK a near this value, together with differences in dissociation behavior among higher pK a charge groups as discussed earlier, could account for discrepancies between our OrgAlk Gran2 and OrgAlk 4.5 observations. Distributions of XT Gran2 , P XT i , and DOC P XT i was generally greater than comparable XT Gran2 (Fig. 4), and both were generally more variable in the Pleasant than the St. John. Differences between P XT i and XT Gran2 may have a number of origins but could be related to the hysteresis between HCl and NaOH titrations of organic material observed by Paxéus and Wedborg (1985). Similar titrations of the same estuary sample in this study using both HCl and NaOH titrants should produce similar hysteresis in the titration curves. Unlike OrgAlk Gran2 and OrgAlk 4.5 , P XT i and XT Gran2 had no correspondence with salinity or season (Fig. 4). The same lack of correspondence was found with organic charge groups 1-3 (Supporting Information). Additionally, P XT i and XT i,Gran2 did not covary with DOC concentrations (Figs. 2, 4). The DOC concentrations along the salinity gradient were consistent among the St. John surveys but demonstrated a clear seasonal shift in the Pleasant estuary, with much higher DOC concentrations at low salinity during the October surveys in comparison to the May surveys (Fig. 2). The Pleasant October surveys were conducted after months of very low precipitation and river flow, which may have resulted in Pleasant river water being comprised of surface runoff, soil porewater, or groundwater that was enhanced in DOC. These higher DOC concentrations were also reflected in the generally higher measured Pleasant estuary OrgAlk Gran2 and OrgAlk 4.5 (Fig. 3).

Alkalinity measured during the NaOH or OrgAlk Gran2 titrations and not attributable to inorganic species is presumably associated with organic charge groups, which should be found in proportion to DOC. But while DOC concentrations generally decreased with increasing salinity, indicating a terrestrial source, P XT i and XT Gran2 either increased or remained approximately constant with increasing salinity. This agrees with Song et al. (2023), who found greater OrgAlk calculated from P XT i and pK ai than OrgAlk Gran2 , and greater seaward P XT i than river P XT i in four of six studied estuaries. These authors attributed this difference to the omission of ionic strength in the charge balance model used to determine P XT i and pK ai . Kerr et al. (2023b) also documented a lack of P XT i variability across a salinity gradient for charge Group 1 (pK a $ 4.8), although charge Group 2 (pK a $ 6.9) did show a more distinct decrease with increasing salinity. These authors suggested tidally driven sediment resuspension may contribute to the addition of organic material, but our DOC results do not show higher DOC led to an addition of P XT i or XT Gran2 . It seems apparent that factors apart from the mixing of high-DOC river water and lower-DOC coastal water are responsible for the distributions or perhaps availability of P XT i or XT Gran2 , and that new analytical methods are needed to better understand the sources and characteristics of organic charge groups. Molecular separation approaches may offer a way to examine the alkalinity contributions and characteristics of broad classes of organics such as humics and fulvics. A new series of dilution experiments using simple organic acids or organic-rich river water (Hinckley 2021) may illuminate Table 3. Organic alkalinity ranges reported by several studies in estuary or coastal ocean systems, the range of salinity ("nr" indicating the salinity was not reported) in each study, the method of organic alkalinity (OrgAlk) determination, and the referring study. The Gran2 and Endpoint 4.5 methods correspond to those described in this work, while the ΔOrgAlk (TA,DIC,pH) method employed measurements of total alkalinity, dissolved inorganic carbon, and pH, together with calculated dissociation constants, to overdetermine the carbonate system and calculate OrgAlk. Negative values are shown in parentheses.

OrgAlk minimum (μmol kg À1 ) OrgAlk maximum (μmol kg À1 ) Salinity range Method Study Satilla estuary 25 115 0-27 Gran2 Cai et al. (1998) Altamaha estuary 10 50 0-32 Gran2 Cai et al. (1998) Savannah estuary 20 40 0-25 Gran2 Cai et al. (1998) Baltic Sea 22 58 3-8 ΔOrgAlk (TA,DIC,pH) Kuli nski et al. (2014) N. Gulf California 0 120 nr ΔOrgAlk (TA,DIC,pH) Hern andez-Ayon et al. (2007) San Diego Bay 100 200 nr ΔOrgAlk (TA,DIC,pH) Hern andez-Ayon et al. (2007) San Quintin Bay 0 70 nr ΔOrgAlk (TA,DIC,pH) Hern andez-Ayon et al. (2007) Gulf of Mexico/Florida (À19) 90 20-38 ΔOrgAlk (TA,DIC,pH) Yang et al. (2015) Gulf of Mexico/Florida 0 40 22-33 Spectrophotometric titration Yang et al. (2015) Baltic Sea (À8) 50 7-14 ΔOrgAlk (TA,DIC,pH) Hammer et al. (2017) Waquoit Bay, Massachusetts 20 80 22-31 Gran2 Song et al. (2020) Six Chinese estuaries 5 65 0-35 Gran2 Song et al. (2023) Dublin Bay 50 230 0-36 Gran2 Kerr et al. (2023a) Rogerstown estuary 40 200 25-33 Gran2 Kerr et al. (2023b) Pleasant estuary OrgAlk Gran2 (À31.9) 110 0-32 Gran2 This study Pleasant estuary OrgAlk 4.5 4 5 2 0 -32 Endpoint 4.5 This study St. John estuary OrgAlk Gran2 7 5 1 1 -30 Gran2 This study St. John estuary OrgAlk 4.5 6 5 5 1 -30 Endpoint 4.5 This study

changes in alkalinity characteristics with changes in ionic strength. These could be coupled with advanced analytical chemistry techniques such as mass spectrometry to examine possible changes in molecular structure along the estuarine gradient. More broadly, a set of analytical best practices is needed in this field bridging inorganic and organic chemical systems. This would allow for better intercomparison of results and less upfront analytical development for researchers new to this topic.

Application of OrgAlk pK a and XT Gran2 or P XT i to pH T estimation One way to assess the success of OrgAlk characterization is to incorporate OrgAlk concentrations and pK a values into carbonate system calculations. If OrgAlk is well characterized, calculated pH T should match measured pH T . The pairing of strictly inorganic parameters (DIC and pCO 2 ) resulted in overestimated pH T in the low and mid salinity estuary regions of both the Pleasant and St. John estuaries (Fig. 5). The DIC and pCO 2 pairing should reflect the influences of inorganic and organic buffers on both the measured pH T and measured equilibrium pCO 2 . The pH T overestimates from input DIC and pCO 2 values were sometimes very large (greater than 2 pH units), particularly in the acidic and organic-rich Pleasant estuary. Pairing Alk Gran1 with DIC or pCO 2 -with no effort to account for OrgAlk-improved pH T retrievals, particularly at low salinity. However, pH T discrepancies larger than 0.50 remained, reinforcing the contention that a portion of titrated alkalinity was not attributable to inorganic carbon, and this affected pH T in a manner that was not reflected by CO2SYS. Including modeled pK a values for each sample and XT Gran2 charge group concentrations slightly improved pH T retrievals when Alk Gran1 was paired with pCO 2 (Fig. 5), but moved calculated pH T from Alk Gran1 and DIC further from observed levels. Finally, substituting P XT i for XT Gran2 resulted in the best pH T retrievals when Alk Gran1 was paired with pCO 2 , but worse retrievals for Alk Gran1 paired with DIC. Lower-pH T Pleasant samples showed more change in calculated pH T with the inclusion of OrgAlk when compared to higher pH T Pleasant samples and St. John samples (Fig. 5). This reinforces the relative importance of inorganic buffering compared to OrgAlk buffering in the two study systems (Supporting Information Section S8, Figs. S4, S5). In the Pleasant sample the in-situ pH T is more strongly buffered by OrgAlk Groups 1 and 2, resulting Offsets in the left panel were calculated using input variables of: dissolved inorganic carbon (DIC) and partial pressure of carbon dioxide (pCO 2 ), initial total alkalinity titration (Alk Gran1 ) and pCO 2 with no organic alkalinity ("no OrgAlk"), Alk Gran1 and pCO 2 with organic alkalinity from Gran2 titrations, ("w/ XT Gran2 "), and Alk Gran1 and pCO 2 with organic alkalinity from NaOH titrations ("w/ P XT i "). Offsets in the right panel were calculated using input variables of: DIC and pCO 2 , Alk Gran1 , and DIC with no organic alkalinity ("no OrgAlk"), Alk Gran1 and DIC with organic alkalinity from Gran2 titrations, ("w/ XT Gran2 "), and Alk Gran1 and DIC with organic alkalinity from NaOH titrations ("w/ P XT i "). Samples circled and marked with "*" and "#" correspond to the data shown in Figs. S2 and S3. Error bars represent the propagated uncertainty of calculated pH T for each sample according to the "High" uncertainties listed in Supporting Information Table S1. The two samples enclosed by the dashed-line box were analyzed before the XT Gran2 and P XT i methods were finalized, thus there are no corresponding pH T offset values for TA (with XT Gran2 ) or TA (with P XT i ). TA, total alkalinity; XT i , organic proton binding site concentration.

in better calculated pH T when OrgAlk is included. In the St. John the in situ pH T is in almost perfect agreement with pK1 DIC , leading to strong DIC buffering at the in situ pH T and little effect of OrgAlk on calculated pH T .

It is worth noting that the Song et al. (2023) version of CO2SYS used in this work does not accept an alkalinity equivalence point input. All organic charge groups given as inputs are treated as proton acceptors (or positive terms in Eq. 2). This approach accounts for all organic proton acceptors that contribute to the observed titration alkalinity. As discussed by Kerr et al. (2023b) this approach is potentially problematic, since the Group 1 pK a is close to the 4.5 equivalence point defined by Dickson (1981). The 4.5 equivalence point dictates that Group 1 charge groups with a pK a above 4.5 are proton acceptors, while those with pK a below 4.5 are proton donors. Thus, most Group 1 charge groups measured in this study should have been apportioned as proton donors (or negative terms in Eq. 2). Given the heterogeneous nature of organic charge groups, the concept of an OrgAlk equivalence point and its application to titration data at pH T lower than 4.5 needs further examination.

The observation that pairing DIC and pCO 2 produced the largest bias in calculated pH T , especially in organic-rich waters at low pH, indicates substantial uncertainties in some aspect of either our measurements or carbonate system calculations. We followed standard ocean best practices for all measurements (see Methods section and Supporting Information), with resulting low estimated uncertainties. We also performed carbonate system calculations that duplicated the approaches and dissociation constants used in other studies. These analytical and carbonate system calculations may merit re-examination in nearshore and estuary settings. Although inclusion of OrgAlk in pH T retrieval calculations resulted in some substantial improvements, the persistent and sizeable pH T offsets that remained illustrate the challenge of carbonate system measurements and calculations in organic-rich estuary systems.

We present some of the first seasonal observations of estuary OrgAlk distributions, measured by different analytic approaches, from two estuaries with contrasting river endmember chemistries. OrgAlk constituted a major part of TA at lower salinities in both estuaries and was an appreciable alkalinity contributor both at higher salinities and in CRM. Distributions of OrgAlk and DOC with salinity varied seasonally in the Pleasant estuary but were seasonally consistent in the St. John estuary. Incremental titrations with NaOH allowed for the estimation of organic acid dissociation constants (pK a ) and total organic charge group concentrations (XT Gran2 and P XT i ). Values of pK a were quite consistent among seasons and between estuaries, and were in general agreement with other studies. Synthesis of measurements of organic pK a values may result in a generalized estimate across systems. However, distributions of XT Gran2 and P XT i did not show an appreciable trend with salinity, estuary, or season. Paired XT Gran2 and P XT i measurements of the same samples also showed a lack of correspondence. Application of XT Gran2 and P XT i , together with pK a values, did not fully explain differences between observed and calculated pH T . The unexplained differences in observed and calculated pH T indicate that analytical methods and carbonate calculations remain challenging in organic-rich estuary systems, and that our understanding of the titration behavior of organic matter is incomplete. Future studies should take a more fundamental approach, by conducting controlled laboratory experiments in which solutions of simple organic acids are mixed with seawater of known composition. These mixtures could be analyzed following the approaches in this work to examine potential changes in titration behavior with salinity. Once the titration behavior of simple organic acids is shown to be predictable, more complex standard organic acids from natural sources could be tested in the same manner. Additionally, the mixed samples could be analyzed using novel methods, such as the optical methods described by Kerr et al. (2023b) or sophisticated molecular characterization techniques such as Fourier transform ion cyclotron resonance mass spectrometry. Finally, a collaborative effort to standardize OrgAlk measurement methods among laboratories is needed for better intercomparison of results.