Implications of salinity normalization of seawater total alkalinity in coral reef metabolism studies

Salinity normalization of total alkalinity (TA) and dissolved inorganic carbon (DIC) data is commonly used to account for conservative mixing processes when inferring net metabolic modification of seawater by coral reefs. Salinity (S), TA, and DIC can be accurately and precisely measured, but salinity normalization of TA (nTA) and DIC (nDIC) can generate considerable and unrecognized uncertainties in coral reef metabolic rate estimates. While salinity normalization errors apply to nTA, nDIC, and other ions of interest in coral reefs, here, we focus on nTA due to its application as a proxy for net coral reef calcification and the importance for reefs to maintain calcium carbonate production under environmental change. We used global datasets of coral reef TA, S, and modeled groundwater discharge to assess the effect of different volumetric ratios of multiple freshwater TA inputs (i.e., groundwater, river, surface runoff, and precipitation) on nTA. Coral reef freshwater endmember TA ranged from -2 up to 3032 μmol/kg in hypothetical reef locations with freshwater inputs dominated by riverine, surface runoff, or precipitation mixing with groundwater. The upper bound of freshwater TA in these scenarios can result in an uncertainty in reef TA of up to 90 μmol/kg per unit S normalization if the freshwater endmember is erroneously assumed to have 0 μmol/kg alkalinity. The uncertainty associated with S normalization can, under some circumstances, even shift the interpretation of whether reefs are net calcifying to net dissolving, or vice versa. Moreover, the choice of reference salinity for normalization implicitly makes assumptions about whether biogeochemical processes occur before or after mixing between different water masses, which can add uncertainties of ±1.4% nTA per unit S normalization. Additional considerations in identifying potential freshwater sources of TA and their relative volumetric impact on seawater are required to reduce uncertainties associated with S normalization of coral reef carbonate chemistry data in some environments. However, at a minimum, researchers should minimize the range of salinities over which the normalization is applied, precisely measure salinity, and normalize TA values to a carefully selected reference salinity that takes local factors into account.


Introduction
Coral reef metabolic measurements are important tools used to quantify a reef's carbon cycle, health and function, and responses to ongoing environmental change. Net reef metabolism (e.g. primary production, respiration, calcification, and CaCO 3 dissolution) is typically quantified through changes in seawater dissolved inorganic carbon (DIC) and total alkalinity (TA) concentrations to determine net ecosystem production (NEP = primary production-total respiration) and net ecosystem calcification (NEC = calcification-CaCO 3 dissolution) [1,2]. Notably, positive coral reef net calcification (i.e., +NEC) is critical for maintaining the calcium carbonate structures and the associated ecosystem services that coral reefs provide [3]. Herein, we evaluate the salinity normalization of TA data and its impact on using alkalinity as a proxy for evaluating coral reef net calcification.
The total alkalinity anomaly technique is pragmatic for determining NEC in coral reefs because TA changes by a factor of two for every unit of CaCO 3 formed or dissolved [4][5][6] with negligible to little influence from other processes (e.g., uptake and release of nutrients) in most coral reef environments [7]. Furthermore, TA is conservative with respect to mixing and changes in seawater temperature and pressure [8]. As a result of reef calcification, TA can vary by upwards of hundreds of μmol/kg across coral reef environments [2]. Consequently, the alkalinity anomaly method, which calculates the difference between initial (e.g., offshore, upstream, or proximal) and final (e.g., coral reef, downstream, or distal) TA can be used to determine whether a reef is net calcifying and combined with measurements of depth and water residence time or transit times to quantify rates of coral reef net ecosystem calcification [5,9]. However, to account for any changes in TA due to freshwater dilution, evaporation, and mixing between water masses, TA data are commonly normalized with respect to changes in salinity, resulting in a salinity normalized alkalinity anomaly (i.e., ΔnTA). Throughout this manuscript, we will use the notation ΔnTA = nTA offshore -nTA reef to maintain consistency, but it is important to note that ΔnTA could represent any nTA initial -nTA final . Salinity normalization of TA is performed using a reference salinity (S ref ), freshwater TA endmember (TA S = 0 ), and salinity (S) data per the following equation [10]: Salinity normalization of seawater TA in coral reef metabolism studies has traditionally used simple dilution concentration (SDC) mechanisms (i.e., freshwater dilution and evaporation) between TA offshore and TA S = 0 = 0 (Eq 1) [10]. However, assumptions regarding SDC can be invalidated by processes that modify freshwater alkalinity such as the weathering of carbonate and silicate minerals [11,12], anaerobic redox processes, and the anthropogenic deposition of sulfuric and nitric oxides as acid rain [13,14]. Coral reefs are complex coastal ecosystems with many potential sources of freshwater TA (i.e., TA S = 0 ) including groundwater (95-13,000 μmol/L [15]), tropical rivers (224-2,156 μmol/L [12]), and precipitation (-2.7-18 μmol/L [14]) such that: where χ represents the relative volumetric freshwater proportion of groundwater (χ gw ), riverine water (χ rw ), or precipitation (χ p ), and their TA concentrations, respectively. If freshwater sources with significant TA S = 0 are volumetrically important, but their concentrations and relative proportions are unknown (Eq 2), the system is underdetermined and could result in errors in both the magnitude and direction of coral reef ΔnTA (Fig 1A-1C). Moreover, in coastal ecosystems such as coral reefs, it is challenging to accurately estimate freshwater alkalinity endmembers (TA S = 0 ), and consequently nTA, from TA-S relationships because evaporation and net calcification further modify TA-S mixing lines [16]. The presence of multiple potential freshwater TA sources and variable mixing ratios co-occurring with biogeochemical modifications of TA raise concerns that unknown TA S = 0 could be a source of significant uncertainty in coral reef ΔnTA estimates and, consequently, estimates of net coral reef calcification rates. In addition to the effects of unknown TA S = 0 on ΔnTA, the application of salinity normalization and the choice of a reference salinity implicitly introduce assumptions about whether conservative mixing occurs before biogeochemical modification (i.e., net ecosystem calcification) or vice versa [16]. For example, Fig 1D and   is normalized to R' and ΔnTA is calculated as the difference in TA between R' and R (Fig 1E). This scenario (S ref = S reef ) implicitly assumes that mixing with the freshwater endmember occurs prior to calcification. The ΔnTA inferred from O and O' is slightly greater than the ΔnTA inferred from R' and R ( Fig 1E). Therefore, the choice of S ref in the salinity normalization of coral reef TA data via Eq 1 implicitly assumes whether calcification occurs before mixing (i.e., S ref = S offshore ), mixing occurs before calcification (i.e., S ref = S reef ), or some order of mixing between these two extremes (i.e., S reef <S ref <S offshore ) and generates an additional source of uncertainty in coral reef ΔnTA.
In a previous study, we suggested that uncertainties in seawater depth and residence time can potentially drive large uncertainties in estimates of coral reef NEC rates while assuming that the accurate determination of TA (±2 μmol/kg) was unlikely to be a significant source of error [17]. Here, we quantify the potential uncertainties in ΔnTA associated with the salinity normalization of coral reef total alkalinity to unknown freshwater endmembers (TA S = 0 ) and reference salinities (S ref ) using global seawater TA and S, fresh submarine groundwater discharge, a range of different TA S = 0 datasets, and different mixing proportions of freshwater endmembers. We provide a series of suggestions to reduce the uncertainties associated with salinity normalization of coral reef TA data with implications for other carbonate chemistry parameters and ions of interest to coral reef metabolism studies (e.g., DIC, Ca 2+ , Mg 2+ , etc.).

Estimating potential coral reef TA S = 0
In the absence of detailed freshwater budgets and relative volumetric proportions of different freshwater TA endmembers in coral reefs, we simulated coral reef TA S = 0 using literature derived data in a Monte Carlo approach (n = 10,000) assuming three distinct scenarios: (i) riverine + groundwater freshwater inputs (Fig 2A); (ii) terrestrial surface runoff + groundwater freshwater inputs ( Fig 2B); and (iii) precipitation + groundwater freshwater inputs ( Fig 2C). For each scenario, a random selection was made from the ratio of fresh submarine groundwater discharge to surface runoff for coral reefs (n = 4,241; Fig 2D) calculated by [18]. We then combined this selected ratio of groundwater inputs value with randomly generated TA concentrations from within the range of the typical coral reef groundwaters (95-13,000 μmol/L [15]), tropical rivers (224-2,156 μmol/L [12]), and precipitation (-2.7-18 μmol/L [14]). This analysis allowed us to simulate the potential TA concentration of mixed freshwater endmembers for each of the three scenarios described above (Fig 2A). The simulated coral reef TA S = 0 were positively skewed so the 50 th , 2.5 th , and 97.5 th percentiles were determined for each of three scenarios to approximate the median and range of potential coral reef TA S = 0 .

Global coral reef total alkalinity data
We used a global assessment of coral reef seawater carbonate chemistry and salinity data [2] to quantify coral reef TA-S relationships, salinity ranges, and the effect of salinity normalization on TA reef . To assess TA-S relationships, type II ordinary least squares linear regression of TA vs. S were constructed for each of the 27 coral reefs using the function lmodel2 [19] in R [20]. To evaluate the range and distribution of salinity changes, we subtracted every salinity value from the maximum salinity value for each of the 27 coral reefs. nTA reef was calculated via Eq (1) using the mean salinity for each site (i.e., S ref = S mean ) and assuming TA S = 0 = 0. We then calculated the difference between TA reef and nTA reef for each of the 27 coral reefs to estimate the magnitude to which salinity normalization changes TA reef data.

Effects of unknown TA S = 0 on ΔnTA
We quantified nTA reef via Eq (1) using the maximum salinity for each site as the reference salinity (i.e., S ref = S max ) and TA S = 0 values of 0, 1000, 2000, and 3000 μmol/kg, which span the full range of potential simulated freshwater TA endmembers in coral reef ecosystems from this study ( Fig 2E). In the absence of reported S offshore for every coral reef location, we assumed that S max represents S offshore to calculate ΔnTA as the mean of TA offshore -nTA reef and ΔS as the mean of S max -S reef for all samples from each reef location in [2]. Furthermore, because the true TA S = 0 for each reef location were unknown, we quantified the uncertainties in ΔnTA owing to mixing within the range of freshwater TA endmembers explored in this study. To accomplish this, we subtracted the ΔnTA values calculated assuming a zero freshwater TA endmember from the ΔnTA values calculated assuming a positive freshwater TA endmember (i.e., ΔnTA TA>0@S = 0 -ΔnTA TA = 0@S = 0 ). Linear regression of these ΔnTA uncertainty vs. ΔS relationships for each TA S = 0 represent the potential range (i.e., uncertainty) in the actual ΔnTA values for a given change in S assuming the true TA S = 0 for each reef site is between the 0 and 3000 μmol/kg values explored in this analysis. To further explore how the precision of S can affect nTA, the minimum difference in reported salinity data for each reef was used to estimate the precision of the salinity measurement.

Effects of unknown order of processes on ΔnTA
To quantify how the implicit order of mixing and biogeochemical processes impact coral reef ΔnTA data, we quantified ΔnTA as either ΔnTA offshore = TA offshore -nTA reef (i.e., S ref = S offshore assuming calcification occurs before mixing; O to O' to R sensu Fig 1E) or ΔnTA reef = nTA offshore -TA reef (i.e., S ref = mean(S reef ) assuming mixing occurs before calcification; O to R' to R sensu Fig 1E) for each reef location in [2]. We then quantified the mean percent difference between ΔnTA offshore and ΔnTA reef for each site to evaluate the type II ordinary least squares linear regression between % ΔnTA uncertainty and ΔS for each reef site using the function lmodel2 [19] in R [20] to see how uncertainty in ΔnTA scales with ΔS owing to the unknown order of mixing and biogeochemical processes.

Coral reef TA S = 0
The global ratio of coral reef fresh submarine groundwater discharge to surface water runoff database [18] provided an opportunity to simulate TA S = 0 for coral reef locations where precipitation, riverine, and freshwater runoff occur in different volumetric proportions (Fig 2). Coral reef TA S = 0 estimates were positively skewed with median (2.5 th to 97.5 th percentile) values of 15 μmol/L (-2 to 1997 μmol/L) for groundwater mixing with precipitation, 1306 μmol/L (293 to 2979 μmol/L) for groundwater mixing with river water, and 598 μmol/L (43 to 2507 μmol/L) for groundwater mixing with surface runoff (Fig 2E). The range of simulations in this study suggest that these uncertainties vary between coral reefs owing to proximity to terrestrially derived freshwater inputs and over time and space within coral reefs owing to temporally and geographically variable freshwater inputs (Fig 2). In particular, assessing the proximity of the reef system to land masses and/or notable surface freshwater inputs could inform which of the three simulated coral reef TA S = 0 (± uncertainty) scenarios explored in this study may best represent uncertainties associated with unknown TA S = 0 in future studies where TA S = 0 and their respective volumetric proportions are unknown. However, we nonetheless caution that these simulations are hypothetical (Fig 2D) and that TA S = 0 may exceed these estimates in select coral reefs with elevated volumetric proportions of groundwater or within individual coral reefs where the assumption of complete mixing between multiple TA S = 0 is invalid. Submarine groundwater discharge can be patchy and heterogeneous across small spatial scales, meaning biogeochemical processes and hydrodynamics should be assessed locally [21,22]. Conversely, the influx of low TA S = 0 owing to precipitation falling directly on the reef and/or adjacent lagoon waters could drive mean freshwater TA S = 0 lower than the simulated values in this study. Moreover, land-based precipitation is likely to reach the reef in the form of runoff, riverine inputs, and/or groundwater at some time lag following the initial precipitation event, suggesting that the timing of precipitation events is an important consideration in estimating the relative volumetric contributions of multiple TA S = 0 sources.

Global coral reef TA-S relationships
We used the global dataset of TA and S data to explicitly test TA-S relationships in coral reef metabolism studies conducted over a broad range of spatial and temporal scales [2]. The majority of coral reefs exhibited detectable linear relationships between TA and S (i.e., 19 of 25 reefs have 95% confidence intervals that do not overlap the dashed 0 line) (Fig 3A and S1  Table), which indicates the need for salinity normalization of TA reef data to account for mixing of water with different properties and the influence of freshwater inputs or evaporation on TA [10]. Notably, data from two reefs exhibited no reported changes in S so the TA-S slopes were undefined for these reef sites and removed from this analysis (i.e., 02 = Mo'orea and 10 = Yonge Reef). Mean ranges in S reef (i.e., S max −S reef ) for each of the reefs varied from 0.05 to 2.1 (mean ± SD for all reefs = 0.5±0.6) (Fig 3B). Mean (±SD) differences between non-normalized and normalized TA (i.e., assuming TA S = 0 = 0 and S ref = S max = S offshore via Eq 1) were -0.2±30.4 μmol/kg (range = -311.9 to +138.2 μmol/kg) (Fig 3C). This mean difference of -0.2 μmol/kg supports previous findings that salinity normalization had a negligible impact on mean ΔnTA across the reef sites presented here [2], especially for reef sites with minimal S ranges (Fig 3B and 3C). However, the range of -311.9 to +138.2 μmol/kg values is the same magnitude as the estimated changes in TA strictly owing to coral reef NEC [17] suggesting

Estimated effects of unknown TA S = 0 on nTA reef
The alkalinity anomalies for each reef location normalized to different TA S = 0 show the potential for non-negligible uncertainties in ΔnTA if a positive TA S = 0 is not accounted for (Fig 4A). Most importantly, the magnitude of the difference between ΔnTA calculated assuming a positive freshwater TA endmember and ΔnTA calculated assuming a zero freshwater TA endmember (i.e., ΔnTA TA>0@S = 0 -ΔnTA TA = 0@S = 0 ) scaled with the magnitude of the difference between S max and S ref (Eq 1 and Fig 4A). Maximum uncertainties associated with freshwater (TA S = 0 ) equal to 1000, 2000, and 3000 μmol/kg compared to TA S = 0 = 0 μmol/kg were 30, 60, and 90 μmol/kg per unit difference in salinity, respectively (Fig 4A). Assuming that TA S = 0 = 0 in the salinity normalization of coral reef TA via Eq 1 can therefore yield uncertainties in ΔnTA that increase linearly with increasing TA S = 0 . Similarly, if TA S = 0 >0 is assumed during salinity normalization, then TA uncertainties increase with increasing offset between TA S = 0 and the assumed TA S = 0 . Establishing potential upper and lower bounds on TA S = 0 for different freshwater endmembers on coral reefs and their relative volumetric contributions to the reef therefore provide an effective means to reduce the potential range of uncertainties associated with the salinity normalization of TA reef (Fig 2E). The canonical assumption that TA S = 0 = 0 for salinity normalization [10] is close to the median TA S = 0 = 15 μmol/L for the precipitation mixing with groundwater scenario in this study, which suggests that TA S = 0 = 0 may remain a reasonable approximation at least for precipitation dominated reef systems and habitats. However, it is important to note that this is from simulated freshwater endmembers in coral reef ecosystems and freshwater TA concentrations can vary considerably in reef ecosystems. Calculating nTA using the full range of TA S = 0 for precipitation dominated systems (i.e., -2 to 2038 μmol/L) may nonetheless provide a more honest assessment of nTA ± uncertainties for cases where TA S = 0 and the relative volumetric freshwater fluxes are unknown.
We recommend viewing coral reefs from an ecosystem-scale perspective to consider the volumetric input of freshwater from different sources (i.e., groundwater, river input, and/or runoff account for a substantial fraction of freshwater input) when using ΔTA as a proxy for coral reef calcification and, if warranted, locate and directly measure TA S = 0 of these freshwater endmembers. However, the multitude of endmembers and biogeochemical processes increasingly complicate estimates of the mixing derived component of coral reef TA reef :S variability. While the estimated freshwater TA endmembers for precipitation, riverine, and runoff dominated systems from this study (Fig 2E) may provide alternative TA S = 0 estimates ± uncertainties wherever the precise quantification of TA S = 0 values and relative volumetric inputs is not feasible, any assumptions regarding the salinity normalization of TA data should nonetheless be carefully considered (e.g., see below list of considerations). Moreover, utilizing other tracers to normalize seawater TA data such as silicate, Ra, Rn, Li, Mg, Sr, Ca, Ba, δ 18 O, and other tracers for submarine groundwater discharge [22][23][24][25] warrant further consideration as additional means to parse out the relative contributions of mixing of multiple freshwater endmembers and biogeochemical fluxes on coral reef seawater carbonate chemistry data.

Effects of unknown order of processes on ΔnTA
The ΔnTA uncertainties owing to the implicitly assumed order of mixing and biogeochemical processes in the salinity normalization of TA were much smaller than the uncertainties owing to the unknown TA S = 0 (Fig 4). For example, there was a 2.8% range of uncertainty in ΔnTA per unit salinity owing to normalizing ocean and coral reef TA data to S offshore compared to S reef (Fig 4B). Assuming an actual 100 μmol/kg alkalinity anomaly solely owing to net calcification, this 2.8% uncertainty per unit salinity translates to a 2.8 μmol/kg uncertainty range, which is similar to the typical precision of ±2 μmol/kg for coral reef TA measurements [17]. The choice of normalizing to S offshore or S reef represent extreme scenarios where either all calcification is assumed to occur before all mixing (S ref = S offshore ) or all mixing is assumed to occur before all calcification (S ref = S reef ) (Fig 1D and 1E). Unless there is information to rigorously evaluate which order of processes is occuring, calculating both ΔnTA offshore using S ref = S offshore (i.e., calcification then mixing) and ΔnTA reef using S ref = S reef (i.e., mixing then calcification) quantifies the maximum uncertainty associated with the unknown order of mixing and calcification processes as follows: Importantly, the average of ΔnTA offshore and ΔnTA reef results in a ΔnTA that assumes net calcification and mixing occur simultaneously and results in a centered, quantifiable ±1.4% uncertainty in ΔnTA per unit salinity change.

Salinity and TA reef variability
In studies aimed at assessing net reef calcification, the simplest way to reduce uncertainties in coral reef nTA is by selecting sampling sites and time periods with minimal S variability (Figs  3 and 4). Selecting sites with known hydrodynamics could further reduce mixing related uncertainties. Any deviations between S offshore and S reef have the potential to generate nonnegligible uncertainties in coral reef salinity normalized total alkalinity anomalies (i.e., ΔnTA = nTA offshore -nTA reef ). While we have assumed that S max = S offshore to fill in missing data from [2], S offshore should ideally be carefully quantified alongside TA offshore to reduce actual ΔnTA uncertainties in subsequent studies. Critically, the choice of sampling location for TA offshore represents an important consideration depending on the aims of the study and characteristics of the coral reef being investigated. For example, choosing an offshore reference that is more proximal to the reef environment can minimize the difference between S offshore and S reef to reduce uncertainties owing to a large range in salinity. Depending on the specifics of individual reef systems and nearshore oceanographic processes, TA offshore of these more proximal offshore waters may be more strongly influenced by other nearshore processes such as upwelling and coastal freshwater inputs [16]. As a result, the choice of sampling location for offshore reference samples is likely context dependent with the capacity to impact both the salinity normalization of TA and the relative contributions of non-reef processes on ΔnTA.
While TA is often evaluated with a high degree of precision and accuracy (i.e., many labs were within ±2 μmol/kg and the majority of labs were within ±10 μmol/kg in a recent intercomparision study; [26]), the estimated precision of reported salinity measurements were �0.01 for 18 reefs, 0.03 for 1 reef, 0.1 for 6 reefs, and undefined for the two reef sites which reported no changes in S. Even small salinity changes of �0.1 across samples can drive significant uncertainties in ΔnTA suggesting that ideally the most precise and accurate S measurement should be used in the evaluation of coral reef ΔnTA. For example, the rounding of 34.44 to 34.4 and 34.45 to 34.5 by a salinity precision of ±0.1 shows how a real 0.01 salinity change can result in an apparent 0.1 salinity change. In this case, normalizing TA to an apparent salinity change of ±0.1 could generate uncertainties up to 9 μmol/kg in nTA values based on the TA S = 0 = 3000 μmol/kg relative to TA S = 0 = 0 μmol/kg scenario. With current salinity sensing technology, uncertainties in salinity and, consequently, nTA could be much smaller. Therefore, any such studies that salinity normalize their TA data may be underreporting the true uncertainties in their measurements by simply stating the precision of their TA measurements and not including the uncertainties owing to their S measurements and subsequent salinity normalization. Furthermore, if changes in salinity are within the reported uncertainties of the salinity measurement, then there is not sufficient evidence that salinity has detectably changed across the reef environment. In these cases, salinity normalization may introduce unnecessary error into TA changes, and it may be more appropriate to avoid salinity normalization if the S range is within the reported precision and/or accuracy of the salinity measurement.

Implications for coral reef net ecosystem calcification
Here we have shown that the uncertainty of ΔnTA measurements is likely greater than the reported ± 2 to 10 μmol/kg precision of TA owing to uncertainties associated with the normalization of TA reef data to S ref and especially if TA S = 0 is unknown. We have further provided quantitative simulations of coral reef freshwater TA endmembers (TA S = 0 ± uncertainties) to approximate the potential uncertainties associated with the salinity normalization of coral reef TA data. We conclude that salinity normalization can change both the sign and magnitude of ΔnTA across coral reef environments suggesting that future studies should exercise caution when evaluating and interpreting ΔnTA from coral reef TA and S data. This is especially true for studies with larger ranges in salinity because the uncertainties associated with ΔnTA positively scale with changes in S. We offer several considerations for salinity normalizing coral reef carbonate chemistry data in the future to reduce potential ΔnTA uncertainties when using the alkalinity anomaly technique as a proxy for net coral reef calcification in any reef system: 1. Do not automatically assume salinity normalization is necessary, as it could introduce more error into your measurements than expected.
2. Examine data for any detectable correlations between salinity and TA as these relationships indicate the potential influence of salinity dilution or concentration mechanisms on TA.
Even if there are no detectable correlations between salinity and TA, evaluate the potential role that simple dilution or concentration mechanisms may have on coral reef TA data.
3. Precisely measure both salinity and TA. Consider the range and precision of your salinity measurements and the potential impact that S normalization has on TA values. If the range in salinity is within the precision of the salinity measurement, consider not salinity normalizing your data.
4. Take a holistic approach to examine possible sources and relative contributions of freshwater and submarine groundwater discharge to the reef system. Consider taking direct freshwater samples to better determine potential endmembers (i.e., TA S = 0 ) that are mixing with the reef water mass to reduce ΔnTA uncertainties and consider avoiding reef metabolism studies in regions with large salinity changes that may confound conclusions regarding ΔnTA.

5.
When the relative volumetric contributions of multiple TA S = 0 are unknown, consider calculating ΔnTA for a range of TA S = 0 values to propagate the potential ΔnTA ± uncertainties owing to unknown TA S = 0 .
6. Carefully select S ref while considering the implicit order of mixing and biogeochemical modification. The mean and range of ΔnTA offshore (i.e., S ref = S offshore ) and ΔnTA reef (i.e., S ref = S reef ) can be used to estimate the ΔnTA ± uncertainties owing to the implicitly assumed order of mixing in the salinity normalization of TA.
7. Propagate the potential uncertainties associated with the salinity normalization of coral reef TA data on calculated ΔnTA to evaluate the relative importance of the salinity normalization process to the resulting estimate of ΔnTA and calculated reef metabolism.
These findings build upon our previous assessment that depth and residence time are the primary sources of NEC uncertainty [17] to include the potentially large uncertainties associated with salinity normalization of TA and DIC data. While this study has focused on coral reef TA for the purpose of brevity, many of these same findings also apply to the salinity normalization of dissolved inorganic carbon (DIC) and other ions of interest (e.g., Ca 2+ , Mg 2+ ) for coral reef metabolism studies, which could be exacerbated depending on their background concentrations in seawater. Reducing uncertainties in the evaluation of coral reef metabolism (e.g. calcification, dissolution, respiration, and photosynthesis) remains critical for observing and quantifying coral reef function and health under unprecedented environmental change.
Supporting information S1 Table. Summary table of [2], method refers to OLS = ordinary least squares regression, term represents the Slope of the relationship, estimate represents the value of the slope, conf.low represents the lower 95% confidence interval of the slope, conf.high represents the upper 95% confidence interval of the slope, and p.value represents the p-value of the slope. (CSV)