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Volume 69, Issue 10 p. 2473-2488
Review
Open Access

Random and systematic uncertainty in ship-based seawater carbonate chemistry observations

Brendan R. Carter

Corresponding Author

Brendan R. Carter

Cooperative Institute for Climate Ocean and Ecosystem Studies, University of Washington, Seattle, Washington, USA

Pacific Marine Environmental Laboratory, National Oceanic and Atmospheric Administration, Seattle, Washington, USA

Correspondence: [email protected]

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Jonathan D. Sharp

Jonathan D. Sharp

Cooperative Institute for Climate Ocean and Ecosystem Studies, University of Washington, Seattle, Washington, USA

Pacific Marine Environmental Laboratory, National Oceanic and Atmospheric Administration, Seattle, Washington, USA

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Maribel I. García-Ibáñez

Maribel I. García-Ibáñez

Instituto Español de Oceanografía, Palma, Spain

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Ryan J. Woosley

Ryan J. Woosley

Center for Global Change Science, Department of Earth, Atmospheric, and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, Massachusetts, USA

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Michael B. Fong

Michael B. Fong

National Institute of Standards and Technology, Chemical Sciences Division, Gaithersburg, Maryland, USA

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Marta Álvarez

Marta Álvarez

Instituto Español de Oceanografía, A Coruña, Spain

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Leticia Barbero

Leticia Barbero

Cooperative Institute for Marine and Atmospheric Sciences, University of Miami, Miami, Florida, USA

Atlantic Oceanographic and Meteorological Laboratory, National Oceanic and Atmospheric Administration, Miami, Florida, USA

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Simon L. Clegg

Simon L. Clegg

School of Environmental Sciences, University of East Anglia, Norwich, UK

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Regina Easley

Regina Easley

National Institute of Standards and Technology, Chemical Sciences Division, Gaithersburg, Maryland, USA

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Andrea J. Fassbender

Andrea J. Fassbender

Pacific Marine Environmental Laboratory, National Oceanic and Atmospheric Administration, Seattle, Washington, USA

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Xinyu Li

Xinyu Li

School of Marine Science and Policy, University of Delaware, Newark, Delaware, USA

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Katelyn M. Schockman

Katelyn M. Schockman

Cooperative Institute for Marine and Atmospheric Sciences, University of Miami, Miami, Florida, USA

Atlantic Oceanographic and Meteorological Laboratory, National Oceanic and Atmospheric Administration, Miami, Florida, USA

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Zhaohui Aleck Wang

Zhaohui Aleck Wang

Marine Chemistry and Geochemistry, Woods Hole Oceanographic Institution, Woods Hole, Massachusetts, USA

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First published: 08 September 2024
Citations: 1

Author Contribution Statement: BRC led project administration, formal analysis, and investigation. BRC led visualization with contributions from JDS. BRC led conceptualization, writing, and editing with contributions from all authors. JDS, MIGI, RJW, and MBF provided extensive contributions to investigation, editing, and review. Each author supplied their own funding and resources.

Associate editor: Christopher Cornwall

Abstract

Seawater carbonate chemistry observations are increasingly necessary to study a broad array of oceanographic challenges such as ocean acidification, carbon inventory tracking, and assessment of marine carbon dioxide removal strategies. The uncertainty in a seawater carbonate chemistry observation comes from unknown random variations and systematic offsets. Here, we estimate the magnitudes of these random and systematic components of uncertainty for the discrete open-ocean carbonate chemistry measurements in the Global Ocean Data Analysis Project 2022 update (GLODAPv2.2022). We use both an uncertainty propagation approach and a carbonate chemistry measurement “inter-consistency” approach that quantifies the disagreement between measured carbonate chemistry variables and calculations of the same variables from other carbonate chemistry measurements. Our inter-consistency analysis reveals that the seawater carbonate chemistry measurement community has collected and released data with a random uncertainty that averages about 1.7 times the uncertainty estimated by propagating the desired “climate-quality” random uncertainties. However, we obtain differing random uncertainty estimates for subsets of the available data, with some subsets seemingly meeting the climate-quality criteria. We find that seawater pH measurements on the total scale do not meet the climate-quality criteria, though the inter-consistency of these measurements improves (by 38%) when limited to the subset of measurements made using purified indicator dyes. We show that GLODAPv2 adjustments improve inter-consistency for some subsets of the measurements while worsening it for others. Finally, we provide general guidance for quantifying the random uncertainty that applies for common combinations of measured and calculated values.

Motivation and background

It is more important than ever to quantify the carbonate chemistry in seawater with well-characterized uncertainty given ongoing and intensifying global ocean carbon accumulation (Gruber et al. 2019; Friedlingstein et al. 2023; Müller et al. 2023), ocean acidification (Doney et al. 2009, 2020), and interest in using and assessing marine carbon dioxide removal strategies (Doney et al. 2022). Well-constrained uncertainties are fundamental for all scientific analyses, and this is especially the case for seawater carbonate chemistry, for which decadal or shorter timescale climate signals are small—often close to analytical detection limits—yet nevertheless quantitatively meaningful for the planetary carbon cycle because they span immense volumes of the ocean.

Uncertainties inherent in seawater carbonate chemistry measurements and calculations have become more quantifiable over time largely due to two developments. First is the increasingly common practice of overdetermining seawater carbonate chemistry with at least three carbonate chemistry variables measured on a single seawater sample, allowing scientists to scrutinize disagreements between measurements and calculations of the variables (McElligott et al. 1998; Kuliński et al. 2014; Chen et al. 2015; Patsavas et al. 2015; Williams et al. 2017; Woosley et al. 2017; Carter et al. 2018; Fong and Dickson 2019; Álvarez et al. 2020; Sulpis et al. 2020; Takeshita et al. 2021; García-Ibáñez et al. 2022; Guallart et al. 2022). Second are the continued improvements in measurement quality; this includes developing and adopting best practices for carbonate chemistry analysis and reporting (Dickson and Goyet 1994; Dickson et al. 2007; Riebesell et al. 2011), the general use of reference materials (RMs; Dickson 2010; Dickson et al. 2003) for total titration seawater alkalinity (AT) and total dissolved inorganic carbon (CT) measurements, and improvements in community measurement practices and equipment (e.g., the production of purified spectrophotometric indicator dyes for seawater pH measurements on the total hydrogen ion scale, or pHT). Because of these developments, consistent patterns in disagreements between measured and calculated values have emerged from the noise of random methodological uncertainties. Importantly, the magnitudes of the disagreements between measured and calculated values rival the magnitudes of contemporary decadal changes in carbonate chemistry from ongoing ocean acidification and other climate change impacts in the open ocean.

Monitoring global change often requires making inferences based on carbonate chemistry calculations, mixing carbonate chemistry measurements with calculations, linking modern measurements to historical measurements (e.g., Carter et al. 2018), and evaluating confidence in measurements and calculations from novel measurement technologies (e.g., Bushinsky et al. 2019). Contending with the uncertainties inherent to carbonate chemistry measurements and calculations is therefore an urgent and perhaps underappreciated challenge for chemical oceanography and metrology. In Supporting Information Text S1, we provide an example of a monitoring challenge where carbonate chemistry uncertainties are a central and urgent challenge.

Definitions for random, systematic, and combined standard uncertainty

As articulated by Newton et al. (2015) (or earlier: Ellison and Williams 2012), uncertainty can be thought of as “a parameter associated with the result of a measurement that permits a statement of the dispersion (interval) of reasonable values of the quantity measured, together with a statement of the confidence that the (true) value lies within the stated interval.” Uncertainty is not the same as measurement error, which is the difference between the true and measured values. For this effort, we use the definition of Newton et al. (2015) and further follow precedent and community recommendations to express our uncertainties as standard deviations (BIPM et al. 2008; Ellison and Williams 2012; Newton et al. 2015; Orr et al. 2018). Thus, if we simplistically assume that the sources of uncertainty result in normally distributed errors, then the 95% confidence interval for the true value would be approximately two standard uncertainties around the reported value (i.e., within ± 2u). We define the terms used to describe aspects of uncertainty in Supporting Information Text S2, where possible using the definitions provided by BIPM et al. (2008) (see also Taylor and Kuyatt 1994). We use u to refer to the combined standard uncertainty or total uncertainty and append subscripts when referring to individual components of the combined standard uncertainty. All terms are represented as standard uncertainties (i.e., the probability distribution of the true error resulting from this contribution to uncertainty can be approximated as a normal distribution with a standard deviation equal to u ).

The chemical complexity and variability of seawater solutions makes overall uncertainty estimation challenging, and analysts and data curators often instead report mean offsets between their measurements of a seawater RM and the reported value (i.e., bias) or statistics from replicate measurements made on a single cruise (i.e., precision). These statistics unfortunately do not capture all sources of variability that contribute to uncertainty (e.g., cruises with different instrumentation, procedures, locations, analysts, etc.). Fortunately, the true value of a variable is not the most critical piece of information for many oceanographic analyses. For example, in a time series of fCO2 calculated from CT and AT, errors in the carbonate chemistry constants may have a meaningful impact on the uncertainty of calculated fCO2 and therefore the air–sea fCO2 difference, but a small impact on the uncertainty of the computed fCO2 trend (this claim is demonstrated with an example calculation in Supporting Information Text S3).

Given this complexity, it is useful to separately quantify “random” components of uncertainty, which result from effects that vary unpredictably within a set of measurements, from the “systematic” components of uncertainty, which are consistent over a set of measurements and lead to offsets relative to the true value or a reference value. The combined standard uncertainty ( u ) then equals the random uncertainty ( u R ) and systematic uncertainty ( u S ) components, expressed as standard deviations, added in quadrature (i.e., the square root of the sum of squares). While the combined standard uncertainty of a parameter ideally accounts for all uncertainty contributions ( u R and u S ), some contributions may cancel for an analysis (e.g., Supporting Information Text S3).

Systematic uncertainty is not the same as bias. A bias is a known systematic offset relative to a reference value that should be corrected; however, the uncertainty in the bias correction (e.g., the uncertainty in the mean value of several measurements of a RM used to derive a bias correction) represents a form of systematic uncertainty that should be included in the calculation of u . It can be challenging to distinguish which offsets between measured and calculated or reference values are biases that should be corrected and which should be treated as the symptoms of quantifiable systematic uncertainties.

The dividing line between random and systematic uncertainties can be unclear. As an example, the sources of uncertainty that we consider to be random between cruises (e.g., day-to-day instrument calibration variations, temperature control errors, sample handling errors) can persist over a set of measurements and contribute to the apparent offset and, thus, to u S . In our analysis, we rely on many different cruises considered collectively, and, with enough randomly distributed cruise offsets, the impact of these offsets should mostly cancel when computing an average offset. We therefore treat these cruise-specific offsets herein as contributions to random uncertainty, but we distinguish between random uncertainty contributions related to the short-term repeatability of measurements ( u Repeatability ) and contributions that vary on longer timescales between cruises u Cruise , thus allowing the cruise-specific variations to be considered as systematic uncertainties when data from a smaller number of cruises are considered. Similarly, the sources of uncertainty that we consider to be systematic (including uncertainties from calibrating a method to an uncertain traceable standard measurement, u Calibration , or incomplete knowledge of seawater acid–base species substance content and thermodynamic constants, u Constants ) can vary with seawater composition and properties and can therefore contribute to the estimated u R in a set of measurements. However, we later show also that these contributions to the random variations are secondary to the measurement and cruise-specific variations for our analysis. The simplifications and terms we use to separate interwoven random and systematic uncertainty components are therefore imperfect, but nevertheless give us a foothold to begin considering how components of uncertainty might affect the full range of possible analyses.

In summary, the combined standard uncertainties u can be computed in two ways:
u 2 = u R 2 + u S 2 (1)
u 2 = u Repeatability 2 + u Cruise 2 + u Constants 2 + u Calibration 2 (2)

We consider u Repeatability to be a component of u R ; u Cruise to be a component of u R when considering many cruises collectively, as we do here, and a component of u S when considering measurements from a single cruise; and u Constants and u Calibration to be primarily contributors to u S . In Supporting Information Text S4, we generate a synthetic dataset visually illustrating each of these uncertainties and showing how u Cruise can act variably as a random or systematic component depending on the data collection considered.

In this paper, we aim to quantify random and systematic uncertainties in the collection of readily available (primarily) open-ocean carbonate chemistry measurements and in calculations made using these measurements. We further explore how the uncertainties we estimate vary between measurements and measurement combinations and how they change when different sets of constants are used for seawater carbonate chemistry calculations. Finally, we propose some guidelines by which one might estimate the combination of random and systematic uncertainties that is most applicable to their analysis.

Methods

Data

Our analysis uses discrete ship-based AT, CT, pHT, and fCO2 measurements and calculations from measurements in GLODAPv2.2022 (Lauvset et al. 2022). This data product is a compilation of datasets from 1085 mostly open-ocean cruises adjusted to improve consistency between cruises. However, we are interested in the data being produced by the community before efforts are taken to improve the coherence of measurements between various cruises, so the first step in our analysis is to reverse the adjustments given in the GLODAPv2.2022 adjustment table (both the data product and the adjustment table are available from www.glodap.info). This step produces the “GLODAPv2.2022_unadjusted” data product.

Seawater carbonate chemistry variables are calculated for all combinations of input pairs for the overdetermined carbonate chemistry measurements in the GLODAPv2.2022_unadjusted data product. Except where noted, these calculations are made using the CO2SYSv3 code for MATLAB® (van Heuven et al. 2011; Orr et al. 2018; Sharp et al. 2021) with carbonic acid dissociation constant parameterizations from Lueker et al. (2000), hydrogen fluoride (HF) thermodynamic constant parameterization from Perez and Fraga (1987), the total boron (BT) to practical salinity (Sp) ratio (BT/SP) from Lee et al. (2010), and the K HSO 4 from Dickson et al. (1990). As pHT and fCO2 are often reported at different temperatures, we follow GLODAPv2 practices and re-compute all measurements and calculations at a standard temperature and pressure of 25°C and 101,325 Pa (i.e., 1 atm, or 0 applied pressure in CO2SYSv3), respectively. The choice of the assumed temperature and pressure has minor impact on the disagreements between measured and calculated values because the conversion affects the measured and calculated values nearly identically. However, the choice does meaningfully impact the propagated uncertainty values because an assumed uncertainty, for example, 0.003 in pHT, can correspond to a different impact on calculated variables at low temperature and high pressure than it does at standard conditions. We rely on standard conditions for our calculations because most prior measurement uncertainty estimates and benchmarks have been obtained from measurements at standard or near-standard conditions. However, we note that uncertainties at in situ conditions are often of greater interest than uncertainties at standard laboratory conditions and urge consideration of how uncertainties might vary at the conditions of interest for an analysis. Despite this relationship between seawater conditions and carbonate chemistry uncertainties, the findings from this study are qualitatively unchanged for calculations at in situ conditions (i.e., the numbers vary, but the claims we make regarding relative uncertainties remain true).

Uncertainty estimates

We use two approaches to quantify both systematic and random uncertainty: uncertainty propagation and inter-consistency comparisons (Fig. 1). The uncertainty propagation estimates are derived by propagating estimates of individual uncertainties in the many measurements and constants used in carbonate chemistry calculations (Orr et al. 2018), whereas inter-consistency estimates are made by comparing measurements of a variable to calculations of the same variable from other measurements. A third approach that we do not consider uses “inter-laboratory comparisons” of measurements from an identical batch of seawater that are made across multiple laboratories (Bockmon and Dickson 2015; Olsen et al. 2019). This approach quantifies uncertainties from methodological variations that exist across the research community, providing bounds on inter-laboratory measurement consistency. However, it only reflects community precision in laboratory measurements and only for a limited number of seawater compositions and laboratories and does not distinguish between labs that do and do not contribute to open-ocean seawater carbonate chemistry data products, and thus does not directly reveal the combined standard uncertainty for open-ocean ship-based discrete carbonate chemistry measurement data products.

Details are in the caption following the image
Conceptual schematic illustrating the process by which random (subscripted as R) and systematic (S) uncertainty ( u ) estimates are obtained for variable V (V) when calculated (C) from variables X (X) and Y (Y). The process is different when the uncertainty is estimated using uncertainty propagation (warm colors, UP) and inter-consistency (cool colors, IC). In the uncertainty propagation approach, a priori estimates of “climate-quality” (Newton et al. 2015) uncertainties in measured (M) values (i.e., u R , M , CQ ) and uncertainties in carbonate chemistry constants ( u Constants ) are propagated to generate random (light orange outline) and systematic (dark orange outline) u estimates in the calculations, respectively. The random uncertainties are then added in quadrature to the climate-quality uncertainty of the measured value for V to estimate the expected random u for the difference between the measured and calculated values of V (i.e., ΔV or Δ). In the inter-consistency approach, measurements of X and Y (i.e., XM and YM) are used along with carbonate chemistry constants (constants) to compute a calculated value of V (VC), which is compared to the associated measured value of V (VM). The average offset between the two is the inter-consistency (IC) estimate of the systematic uncertainty ( u S , Δ , IC , V ) in this difference. The 68th percentile of the spread in the residuals ( u R , Δ , IC , V ) around the u S , Δ , IC , V is the result of the random measurement uncertainty in V (i.e., u R , M , V ) and the random uncertainty in the calculated value of V ( u R , C , IC , V ) added in quadrature.

Due to the variety of uncertainty terms discussed and the need for specificity, we refer to uncertainties using several subscripts given in Table 1, for example, u S , C , UP , AT , where u with a subscript indicates an uncertainty contribution, “S” indicates the u is systematic, “C” indicates a calculated variable, “UP” indicates estimation through uncertainty propagation, and “AT” means the uncertainty is specific to AT.

Table 1. Subscripts used herein for u and their explanations.
Position ( u 1 , 2 , 3 , 4 ) Subscript Meaning
1 R Random
1 S Systematic
2 M Specific to a measurement
2 C Specific to a calculation
2 Δ Specific to a difference between a measurement and a calculation
3 UP Estimated using uncertainty propagation
3 IC Estimated using inter-consistency calculations
3 CQ Assumed to be “climate-quality”
4 V Applies to variable of interest “V
4 X Applies to variable “X” used with variable “Y” to calculate variable of interest V
4 Y Applies to variable “Y” used with variable “X” to calculate variable of interest V
4 AT Applies to total titration seawater alkalinity (AT)
4 CT Applies to total dissolved inorganic carbon (CT)
4 pHT Applies to seawater pH on the total hydrogen ion scale (pHT)
4 fCO2 Applies to the fugacity of CO2 in a headspace in gas-exchange equilibrium with the seawater (fCO2)

Uncertainty propagation

Significant progress has been made in recent years toward estimating reasonable uncertainties for the measurements and constants used in seawater carbonate chemistry calculations (Table 2, with references therein) and propagating these uncertainties to compute uncertainty in calculated quantities. Notably, Orr et al. (2018) released code that propagates user-provided uncertainties, which has been incorporated into recent releases of carbonate chemistry software (Orr et al. 2018; Sharp et al. 2021; Humphreys et al. 2022). Likewise, inter-consistency has long been used for estimating carbonate chemistry uncertainty, and the GLODAPv2.2022 data product update includes discrete fCO2 measurements (Lauvset et al. 2022) providing new opportunities for these comparisons (e.g., García-Ibáñez et al. 2022).

Table 2. Literature-estimated values of the combined standard uncertainty (or the total relative uncertainty expressed as a percentage) of the indicated constraints for the carbonate chemistry in oxygenated seawater. Combined standard uncertainty and other terms used herein are defined in the glossary. Where no estimate of combined uncertainty is yet available, random uncertainty has been given. Random uncertainty is given in addition to the uncertainty in several instances in which both have been assessed. These estimates are most appropriate for a salinity of ~ 35, a temperature of ~ 25°C, and a total pressure of 1 atm. For a comparison in this study, terms in bold are propagated to obtain systematic uncertainty estimates while the other quantities, as given in the random uncertainty column, are propagated for random uncertainty estimates. We consider all uncertainties in these constants as contributors to systematic uncertainty in our calculations.
Parameter Combined standard uncertainty Random uncertainty Reference(s)
AT 2 μmol kg−1 2 μmol kg−1 Orr et al. (2018); Newton et al. (2015)
CT 2 μmol kg−1 2 μmol kg−1 Orr et al. (2018); Newton et al. (2015)
pHT 0.01 0.003 Orr et al. (2018); Newton et al. (2015)
fCO2 1% 0.5% García-Ibáñez et al. (2022); Newton et al. (2015)
PhosphateT * 2% Lauvset et al. (2022)
SilicateT * 2% Lauvset et al. (2022)
ST 0.16% 0.005 g kg−1 Morris and Riley (1966); Lauvset et al. (2022)
BT 2% * Orr et al. (2018)
FT 0.15% * Warner (1971)
pKW 0.01 * Orr et al. (2018)
pK1C 0.0075 0.0055 Orr et al. (2018)
pK2C 0.015 0.010 Orr et al. (2018)
pKB 0.005 * Dickson et al. (1990)
pK1P 0.034 * Dickson and Riley (1979)
pK2P 0.015 * Dickson and Riley (1979)
pK3P 0.17 * Dickson and Riley (1979)
pKSi * 0.02 Millero (1995)
pKS * 0.01 Dickson et al. (1990)
pKF * 0.02 Dickson and Riley (1979)
pK0 0.002 * Orr et al. (2018)
  • * Value unknown.

We use the CO2SYSv3 uncertainty propagation code (Sharp et al. 2021; adapted from Orr et al. 2018) to quantify how input uncertainties in the carbonate chemistry calculations impact the calculated outputs (Fig. 1). For the systematic uncertainty propagation calculations ( u S , C , UP ), we use the carbonate chemistry and other constant uncertainties suggested by Orr et al. (2018) (i.e., the bolded terms in Table 2). For the random uncertainty propagation calculations ( u R , C , UP ), we use the random uncertainty estimates (i.e., random measurement terms in Table 2 associated with “climate-quality” measurements from Newton et al. (2015)). Newton et al. (2015) defined climate-quality measurements as those capable of resolving changes in carbonate ion contents with a relative standard uncertainty of less than 1% and suggest this translates to standard uncertainties of 2 μmol kg−1 in CT and AT, 0.003 in pHT, and a relative uncertainty of 0.5% in fCO2. Critically, this “climate-quality” definition implicitly omits the contribution of systematic uncertainty in measurements because it is based on resolving changes rather than quantifying true values. It is therefore a metric for random uncertainty ( u R ).

We calculate random uncertainties for the differences ( u R , Δ , UP ) between measurements (M) and calculations (C), assuming the measurement also meets climate-quality (CQ) criteria, by taking the positive square root of the sum of the squared uncertainties:
u R , Δ , UP = u R , C , UP 2 + u R , M , CQ 2 (3)

This equation applies equally to terms later calculated for inter-consistency calculations (IC), and allows u R , Δ , UP estimates to be compared to random uncertainties from the inter-consistency analysis that—by necessity—include uncertainties from both measurements and calculations. As we do not separately account for systematic uncertainty in the measurements, u S , Δ , UP equals u S , C , UP .

Uncertainty propagation estimates themselves vary with sample composition (see Woosley and Moon 2023). We propagate uncertainties for all measurements individually, but, for simplicity, present the means of these propagated uncertainties (and, in one instance, their statistics) for collections of measurements in our figures and tables. We justify the omission of u Constants from u R , C , UP and note three nuances that are important for interpreting our uncertainty propagation estimates in Supporting Information Text S5.

Inter-consistency comparisons

We estimate random and systematic contributions to combined uncertainty with an “inter-consistency” analysis using collections of overdetermined carbonate chemistry measurements (Fig. 1). There are several steps for these calculations, and all of them are repeated for all combinations of four variables of interest “V” (AT, CT, pHT, and fCO2) and for each of the three combinations of choices for variables “X” and “Y” that can be used to calculate each V (for 12 total combinations of V, X, and Y).
  1. For each measurement of V (VM), we calculate values of V (VC) from X and Y.
  2. Residuals (ΔV) are computed between the measured and calculated values:

    Δ V = V M V C (4)

  3. The inter-consistency-based estimate of the systematic component of uncertainty in Δ V (i.e., u S , Δ , IC , V ) is computed as the mean ΔV across all samples in the data product. These inter-consistency-based estimates of systematic uncertainty do not distinguish between systematic uncertainty in measurements ( u S , M , IC , V ) and calculations ( u S , C , IC , V ) of V and only reflect their apparent offset. Supporting Information Text S6 offers discussion of the implications of calculating u S , IC in this fashion.
  4. The inter-consistency-based estimate of the random component of uncertainty in ΔV (i.e., u R , Δ , IC , V ) is a measure of how much spread in ΔV values exists around the mean ΔV (i.e., around u S , Δ , IC , V ). It is estimated as the 68th percentile of absolute deviations between ΔV values and u S , Δ , IC , V . We use the 68th percentile in place of the standard deviation here because the ΔV differences are not normally distributed. We justify this choice and briefly discuss its implications in Supporting Information Text S7.
  5. For discussion purposes, we repeat these calculations using variations and subsets of the full collection of overdetermined measurements (mapped in Supporting Information Fig. S1) including:

    1. the GLODAPv2.2022 data product with the secondary quality control (QC) adjustments included,
    2. three subsets where spectrophotometric pHT measurements were made using purified indicator dyes, using indicator dyes that have not been purified, and using potentiometric or unknown pHT measurement methods,
    3. and the subset of GLODAPv2.2022 with a QC flag of 0 indicating secondary QC was not attempted.

Quantifying measurement uncertainties

So far, we have used inter-consistency comparisons only to quantify uncertainties in the differences between measured and calculated seawater carbonate chemistry variables, but we are also interested in using inter-consistency to estimate uncertainties in the measured and calculated values individually. In principle, we can leverage our 12 sets of inter-consistency calculations to go beyond our simplistic assumption of climate-quality measurements: we can rewrite Eq. 3 for the IC terms and expand the u R , C , IC , V term to reflect contributions from random uncertainties in measurements of the variables “X” and “Y” used to calculate “V” multiplied by sensitivity terms for the calculated value (i.e., V C X and V C Y ), and a term u Other that reflects the contributions of random uncertainties in all other inputs to carbonate chemistry calculations (e.g., temperature, salinity, and dissolved inorganic nutrient contents. Note: this u Other term is also specific to the combination of V, X, and Y and the sample composition despite the absence of detailed subscripts in our notation). The sensitivity terms are calculated for each overdetermined sample individually by perturbing the input value for the calculation by (adding) the random uncertainty values in Table 2 and recalculating V. These sensitivities are then averaged across all measurements to obtain mean values used to calculate u R , Δ , IC , V :
u R , Δ , IC , V 2 = u R , M , V 2 + V C X u R , M , X 2 + V C X u R , M , Y 2 + u Other 2 (5)

Equation 5 can be written for each of the 12 combinations of V, X, and Y considered and the resulting system of 12 equations can be solved for four unique random measurement uncertainties u R , M for each of the four variables (the sensitivity terms and u Other , V can be calculated using uncertainty propagation and averaged across the measurements in the GLODAPv2.2022_unadjusted product). However, in practice, these calculations are not well conditioned despite the 12 constraining equations and only 4 unknowns. This is because the impacts of uncertainties in AT and CT measurements are nearly colinear, and a similar statement can be made for the impacts of uncertainties in pHT and fCO2 measurements. Also, disagreements between pHT measurements and pHT calculated from CT and AT provide similar information to the disagreements between CT measurements and CT calculated from pHT and AT. Similar statements can be made for other combinations.

To compare the quality of the measurements of a value V to the desired quality, we introduce dimensionless ratios between the estimated ( u R , M , V ) and the desired climate-quality ( u R , CQ , V ) uncertainties:
r V = u R , M , V u R , CQ , V (6)

We solve for the r V ratios that minimize the apparent disagreement between the observed u R , Δ , IC using methods detailed in Supporting Information Text S8. Due to the difficulty of distinguishing the effects of uncertainty in CT from uncertainty in AT, we require the simplifying assumption that the r CT and r AT values approximately equal each other.

Results and discussion

Random uncertainty in calculations ( u R , C )

Figure 2 shows distributions of residuals for GLODAPv2.2022_unadjusted data product (gray histograms) between measured and calculated values (i.e., ΔV) along with Gaussians representing random uncertainty distributions determined from inter-consistency ( ± u R , Δ , IC , blue lines) and from uncertainty propagation ( ± u R , Δ , UP , Eq. 3, orange lines), both centered on systematic uncertainties determined from inter-consistency ( u S , Δ , IC ). These figures are also provided for the GLODAPv2.2022 data product with adjustments (Supporting Information Fig. S2). The uncertainty propagation estimates (orange lines) imply a tighter distribution of residuals between measured and calculated values than is found in practice through inter-consistency comparisons (blue lines). It can also be seen that most of the residual distributions are not well-approximated as a normal distribution, implying that the data from the GLODAPv2.2022_unadjusted data product are heterogeneous with respect to random uncertainties.

Details are in the caption following the image
Uncertainty estimates represented as equal area Gaussian distributions plotted over a histogram (also of equal area to the Gaussians) of residuals between the indicated measurements and calculations from the GLODAPv2.2022_unadjusted data product (i.e., after removing the GLODAPv2 inter-cruise consistency adjustments). The blue Gaussian lines are centered on the mean inter-consistency residual (i.e., the u S , Δ , IC ) and have widths set to match the 68th percentiles of these residuals around the mean residuals (i.e., u R , Δ , IC as in Fig. 1). The orange Gaussians are also centered on the mean residual and have a width set equal to the uncertainty propagation based random uncertainty estimates for calculations u R , C , UP (Eq. 3) after adding the climate-quality measurement uncertainty u R , M , CQ in quadrature to account for the added uncertainty in the measurement used to compute the residual. See the text for a discussion regarding the comparative widths of the blue and orange lines. A dotted vertical line at 0 is provided for reference. All comparisons are made at 1 atm and 25°C. Note the different number of measurements (N) for each pair.

Figure 3 shows “random uncertainty” estimates for calculations obtained from both inter-consistency (blue bars, u R , Δ , IC ) and uncertainty propagation (orange bars, u R , C , UP ), equivalent to the 68th percentile widths of the Gaussians in Fig. 2. Figure 3 reaffirms that some combinations of measurements are better for calculating a given seawater carbonate chemistry variable (i.e., have shorter bars) than others. Calculations that use the pHT and fCO2 pair together are particularly problematic, and calculations that pair either AT or CT with either pHT or fCO2 are generally best. This is consistent with long-established principles regarding whether two measurements provide similar or independent information for constraining the seawater carbonate chemistry (e.g., Dickson and Riley 1979; Millero 2007; Cullison Gray et al. 2011; McLaughlin et al. 2015).

Details are in the caption following the image
Bar plots of estimated random standard uncertainties for residuals between measurements and calculations estimated from inter-consistency calculations ( u R , Δ , IC , blue bars) and uncertainty propagation ( u R , Δ , UP , orange bars) for the seawater carbonate chemistry variables listed on the y-axes (in the indicated units) when calculated using the pairs of measurements listed on the x-axes on either side of the bars. Of note, the blue bars are always greater than the associated orange bars. The whiskers on the orange bars indicate 1 standard deviation of the range of u R , Δ , UP values obtained from the measurements in the GLODAPv2.2022_unadjusted data product, with the variability being attributable to the varying sensitivity of the calculations to assumed uncertainties in the input measurements as the seawater composition changes across the various measurements in the data product. In keeping with others (Newton et al. 2015; García-Ibáñez et al. 2022), fCO2 is quantified as a relative precision (percentage of the measured value). Seawater pHT is seawater pH on the total hydrogen ion scale. All comparisons are made at 1 atm and 25°C. Calculations use the default carbonate chemistry constants for this analysis (Lueker et al. 2000; Lee et al. 2010).

As noted, the u R , Δ , IC estimates are always worse than the u R , Δ , UP estimates, ranging from ~ 1.5 to ~ 2.3 times (average 2.0 times) as large across the various calculations (Fig. 3). This implies at least one of two unfortunate possibilities: (1) these measurements within GLODAPv2.2022, considered collectively, are not attaining the stringent climate-quality precision standard or (2) there are unknown gaps in our understanding of the seawater carbonate chemistry and other seawater acid–base systems. One known gap in our understanding of carbonate chemistry relates to the presence of organic or other unidentified contributions to AT (see Carter et al. (2024) for further discussion) and it is likely that these species contribute both to systematic and (through spatial or temporal variations in their amount contents in seawater) random uncertainties. When provided in cruise reports, most hydrographic cruise data QC metrics (e.g., from replicates and measurements of RMs) do not give clear evidence—nor do they typically give any reason to doubt—that the measurements provided are climate-quality, so we contend that both options are possible.

For discrete fCO2, the comparison comes from only 14 cruises (with a 15th eligible cruise omitted, GLODAPv2.2022 cruise number 695, because it appears to be an outlier and including it nearly doubles the standard deviation of the measurement and calculation residuals). These comparisons therefore should be given lower confidence relative to comparisons that do not involve fCO2, which are compiled from far more cruise datasets.

Like García-Ibáñez et al. (2022), we note that random uncertainty estimates from inter-consistency improve by an average of 22% for combinations of pHT, CT, and AT when the GLODAPv2.2022 secondary QC adjustments are included (Supporting Information Fig. S3), while random uncertainty estimates involving both fCO2 and pHT worsen by an average of 58% when the adjustments are included. The adjustments improved inter-consistency between AT, CT, and fCO2 by an average of 7%. While the fCO2 data could not be adjusted during secondary QC due to sparse data, for some cruises, the data that they are compared to (i.e., AT, CT, and pHT) are adjusted. Our results therefore reinforce the idea that GLODAP data product consistency adjustments are making the pHT and fCO2 measurements less inter-consistent (see García-Ibáñez et al. 2022 and Supporting Information Fig. S3).

The subset of pHT measured on 47 cruises that used the spectrophotometric method with purified m-cresol purple indicator dyes has unusually strong inter-consistency, with 38% smaller average u R , Δ , IC , pHT values than the data product at large (Supporting Information Fig. S4 compared to Fig. 3). The u R , Δ , IC , pHT estimate from the CT and AT combination is only 20% greater than the u R , Δ , UP , pHT estimate. In Supporting Information Text S9, we discuss a subset of the GLODAPv2.2022 data product that was not subjected to the secondary QC with higher than average u R , Δ , IC values.

Systematic uncertainty in calculations ( u S , C )

In our companion paper (Carter et al. 2024), we discuss many sources of uncertainty that collectively give rise to systematic offsets. However, in contrast to the estimates of random uncertainties, the inter-consistency based systematic discrepancies between measurements and calculations ( u S , Δ , IC ) for seawater carbonate chemistry variables in GLODAPv2.2022_unadjusted data product fall within the interval defined by the standard uncertainties that would be expected to result solely from assumed uncertainties in carbonate chemistry and other constants ( u S , Δ , UP ). Supporting this, the orange whiskers in all uncertainties reflecting ± u S , Δ , UP contain the u S , Δ , IC estimates in all instances in Fig. 4. This is also true for many but not all the u S , Δ , IC estimates obtained when using alternative constant sets (Supporting Information Text S10). Systematic uncertainty from carbonate chemistry constant sets therefore warrants further quantitative consideration.

Details are in the caption following the image
u S , Δ , IC Estimates obtained from the GLODAPv2.2022_unadjusted data product plotted as blue bars for the indicated combinations of variables used to calculate the variable of interest. The adjacent orange lines indicate the range of ± u S , Δ , UP (1σ) around the x-axis (black line). Seawater pHT is seawater pH on the total hydrogen ion scale. All comparisons are made at 1 atm and 25°C. Calculations use the default carbonate chemistry constants for this analysis (Lueker et al. 2000; Lee et al. 2010).

Carbonate chemistry constant set comparisons

In recent years, a community consensus has emerged favoring the use of the carbonic acid dissociation constants measured by Mehrbach et al. (1973) and re-parameterized by Dickson and Millero (1987) on the seawater pH scale or by Lueker et al. (2000) on the total pH scale (Raimondi et al. 2019 and many references cited; Woosley 2021; Jiang et al. 2022), though the community consensus is less established for polar (Sulpis et al. 2020; Gattuso et al. 2023 and references therein) and coastal waters. Our calculations allow us to build upon this discussion by comparing the carbonate chemistry constants across multiple variables and calculations for the body of oceanographic measurements available in GLODAPv2.2022_unadjusted data product, as Woosley (2021) and Woosley and Moon (2023) did recently for AT, CT, and pHT measurements from their laboratory. We provide some insights from our comparisons in Supporting Information Text S10. However, it is important to state that inter-consistency is not a measure of accuracy and having a small u S , Δ , IC or u R , Δ , IC does not guarantee a better value. This is because unidentified systematic uncertainties can significantly impact the results (Fong and Dickson 2019; Woosley and Moon 2023). For this reason—and because our findings vary with the data used, inter-consistency comparison variables considered, and the inclusion or omission of adjustments—we refrain from recommending a single carbonate chemistry constant set on the basis of this analysis and instead note that many community recommendations (by, e.g., Lee et al. 2000; Jiang et al. 2022; Sutton et al. 2022; Woosley and Moon 2023) advocate for constant sets that we find to be comparably inter-consistent (Supporting Information Text S10).

Random uncertainties in measurements in GLODAPv2.2022_unadjusted data product

Until now, we have only been able to say that the disagreements between measured and calculated values are larger than we would expect if all seawater carbonate chemistry measurements were being consistently measured at climate-quality by the community contributing to the GLODAPv2 data product. The various r V ratio calculations allow us to go further and estimate the random uncertainties for measurements of individual variables ( u R , M ), which can then be propagated to estimate the random uncertainties for calculated values ( u R , C ), in the GLODAPv2.2022_unadjusted data product (Table 3). We recommend the uR,M values in Table 3 as more realistic community-level random measurement uncertainty estimates than the climate-quality values. Users can adopt these u R , M values for uncertainty propagation with their specific measurements and seawater compositions of interest.

Table 3. Random and systematic uncertainties in the GLODAPv2.2022_unadjusted data product and subsets thereof, estimated as indicated in the text. Values in italicized text are assumed whereas values in plain text are calculated. A dash indicates an estimation that is not attempted. u R , M stands for random measurement uncertainty and u R , C stands for random calculation uncertainty. u R , C varies with seawater composition and should be recalculated for seawater conditions of interest in an analysis. Units for AT and CT are μmol kg−1, pHT is unitless, and fCO2 uncertainties are expressed as a percentage.
Estimate for r AT = r CT r pHT r fCO 2 u AT CT pHT fCO2
Estimates of random uncertainty for measurements in GLODAPv2.2022
Assumed climate-quality 1 1 1 u R , M , CQ 2 2 0.003 0.50
All data 1.2 3.6 3.9 u R , M 2.4 2.4 0.011 1.9
Subset: spec. pHT 1.0 3.5 u R , M 2.0 2.0 0.010
Subset: pure dye spec. pHT 1.9 u R , M 0.006
Subset: impure dye spec. pHT 3.3 u R , M 0.010
Subset: potentiometric pHT 2.1 4.7 u R , M 4.2 4.2 0.014
Estimates of random uncertainties in calculations from GLODAPv2.2022_unadjusted
calcs. from AT and CT using values from the “all” category above u R , C 0.008 1.8
calcs. from AT and pHT u R , C 3.2 1.5
calcs. from AT and fCO2 u R , C 2.2 0.003
calcs. from CT and pHT u R , C 3.3 1.4
calcs. from CT and fCO2 u R , C 2.7 0.003
calcs. from pHT and fCO2 u R , C 38.8 34.6 -

If we solve for a single r—or ratio of the true random uncertainty to the climate-quality uncertainty that best aligns the uncertainty propagation and inter-consistency random uncertainties—for all equations and all variables then we would obtain a value of 1.7 for all data in the GLODAPv2.2022_unadjusted data product. This is a quantitative restatement that the apparent scatter in the differences between measurements and calculations is greater than expected from uncertainty propagation. The same is true when the r is derived after excluding the comparisons that use fCO2 information ( r = 1.8 ). This suggests that the issue is not limited to the comparatively few new-to-GLODAP cruises with discrete fCO2 measurements. Interestingly, the GLODAPv2.2022 adjustments would improve the r calculated for the system of equations relating AT, CT, and pHT (which decreases from 1.8 to 1.5 when adjustments are included) but worsen the r calculated for the system of equations that relates all variables (which increases from 1.7 to 2.0). This implies that the adjustments are indeed improving internal consistency between AT, CT, and pHT, but they are also moving the carbonate chemistry data further from the constraint provided by the fCO2 data.

The r AT , r CT , and r pHT ratios are calculated to attribute the uncertainty to AT and CT collectively or to pHT separately. In Table 3, we see that the uncertainty propagation and inter-consistency estimates are best aligned for all AT, CT, and pHT when pHT is assigned an uncertainty that is a larger multiple of the climate-quality uncertainty ( r pHT = 3.6 ) than the other two variables ( r CT = r AT = 1.2 ). This is not surprising given that pHT has been measured in the absence of a seawater RM using varied techniques that have evolved methodologically over the decades covered by the GLODAPv2.2022 data product (see Supporting Information Text S1), and the development of a RM for seawater pH remains a noted priority (Capitaine et al. 2023). By contrast, AT and CT measurements have comparative methodological consistency and the benefit of a widely-used seawater RM. We can go further by examining the r pHT values obtained for subsets of the seawater pHT measurements. The ratio is largest ( r pHT = 4.7 ) for non-spectrophotometric seawater pHT measurements (e.g., potentiometric measurements or where the method used is unspecified in the metadata data product of Carter et al. (2024)). Considering only spectrophotometric seawater pHT measurements made using unpurified indicator dyes improves the ratio ( r pHT = 3.3 ). Limiting the comparison to those made only using purified indicator dyes improves the ratio even more ( r pHT = 1.9 ). Interestingly, the combination of both spectrophotometric measurement types ( r pHT = 3.5 ) is worse than either individually, implying that unpurified indicator dye measurements, while more variable than purified indicator dye measurements, are more consistent with each other than they are with purified indicator dye measurements.

The r CT and r AT value (1.0 ± 0.2) is indistinguishable from 1 for the subset of measurements paired with spectrophotometric pHT measurements, implying that the associated AT or CT measurements have random uncertainties comparable to the climate-quality thresholds. By contrast, the r pHT value of 1.9 implies a random uncertainty of ~ 0.006 for spectrophotometric seawater pHT measurements made with purified indicator dyes, and the r fCO 2 value of 3.9 implies a random uncertainty of 2% in fCO2 measurements, both of which are greater than the climate-quality thresholds (Table 3). However, we contend that values of the climate-quality thresholds for pHT and fCO2 could be plausibly quantified as ~ 0.005 for pHT and ~ 1.5% for fCO2 (instead of the nominal values of 0.003 for pHT and 0.5% for fCO2). This is because changes of these magnitudes result in the 1 % carbonate ion content change used to define climate-quality measurement criteria except when pairing pHT with fCO2 in the carbonate ion content calculation (which is not recommended when an alternative measurement combination is available). Unfortunately, for all subsets, the random uncertainties from any two measurements used in a calculation invariably result in random calculation uncertainties that are greater than the climate-quality thresholds (Table 3).

Random uncertainties and the adjusted GLODAPv2.2022 data product

Given the mixed impact of GLODAPv2.2022 adjustments on the inter-consistency of different carbonate chemistry variable pairings, we do not separately estimate random uncertainties for the adjusted data product and suggest using the uncertainty estimates in Table 3 regardless of whether adjustments are retained. We recommend that the GLODAPv2.2022 adjustments be retained when consistency between measurements of individual carbonate chemistry variables across multiple cruises (which is quantifiably improved by the adjustments; Lauvset et al. 2022) or inter-consistency between AT, CT, and pHT are of primary interest.

We contend our random uncertainty estimates largely reflect semi-random cruise-specific offsets rather than simple random variations that are unique to each measurement (compare Supporting Information Fig. S5c,d). Despite this, our random uncertainty estimates are smaller than the adjustment limits used by the GLODAPv2 reference team for deciding when to apply adjustments to eliminate cruise-specific offsets and thereby improve internal data product consistency. This is because a cruise can only be said to be significantly different from the existing collection when it differs by a statistically significant amount. If we use the approximation of normally distributed variations between cruises, a cruise could be considered different with meaningful confidence when its mean offset is > 2σ, or > 2 u R , M , IC , from the mean of multiple other cruises. Thus, this study supports the current adjustment limits of 4 μmol kg−1 in AT and CT, which are approximately double the u R , M estimates (Lauvset et al. 2022), but indicates that the pHT adjustment limit of 0.01 is low relative to the u R , M , pHT (2σ = 0.014–0.030).

Determining the standard uncertainty to use for an analysis

As some systematic uncertainty contributions to the combined standard uncertainty can cancel for an analysis exploring temporal or spatial changes, it can be challenging to know when to include various uncertainty contributions in an analysis. In Table 4, we provide general guidelines for how these decisions might be made for several common types of analysis. An added complexity in this table, noted earlier, is that the u R , M reflects a combination of random variations that are specific to each measurement ( u Repeatability ) and random variations that are specific to a cruise but uniform across the measurements from the cruise ( u Cruise ). It can be important to distinguish between these contributions to u R , M for some analyses. Examples include observing system simulation tests of how well a given analysis can extract an exactly-known modeled signal from model output that has been perturbed with simulated measurement uncertainties, or any analysis that uses a Monte Carlo perturbation to assess the likely impacts of measurement uncertainties. An example calculation using this approach that also demonstrates the importance of considering cruise-wide offsets (i.e., u Cruise ) separately from measurement repeatability (i.e., u Repeatability ) is provided as Supporting Information Text S11.

Table 4. Guidelines for estimation of random uncertainty ( u R ) for analyses that rely on various collections of measured and calculated values. Subscripts for u values are given in Table 1. Values for various terms are given in Figs. 3, 4 and Table 3. These uncertainties should be propagated through calculations used by the analyst. The u S , Δ , UP should also be considered as a source of systematic uncertainty even when it is included below.
Information used u R
Measurements made on a single cruise See cruise report for u Repeatability estimate or conservatively use u R , M (Table 3)
Measurements within a region measured by multiple cruises u R , M (Table 3)
Calculations within a region measured by multiple cruises u R , C (Table 3)
Combination of measurements and calculations u R , M 2 + u R , C 2 + u S , Δ , UP 2 (Fig. 4; Table 3)
Calculations of differences relative to a threshold value (e.g., air–sea ΔfCO2 or time spent with an Ω > 1), here u Thresh refers to uncertainty in the threshold value u R , M 2 + u S , Δ , UP 2 + u Thresh 2 (Fig. 4; Table 3)
Non-discrete measurements, or calculations from such measurements (e.g., autonomous sensors) As in associated rows above, but with different u values than those estimated herein.

As we do not, from this analysis, have a reason to favor any set of carbonate chemistry constants to the exclusion of the others, and the choice of carbonate chemistry constant sets has a large impact on the calculated u S , C , IC (Supporting Information Text S10), we do not believe our u S , C , IC estimates are robust. We therefore recommend the use of u S , C , UP instead of u S , C , IC in Table 4.

Conclusions

Uncertainty quantification in seawater carbonate chemistry variables is complicated due to the large variety of variables that are measured, calculated, and estimated to constrain seawater carbonate chemistry; evolving measurement protocols for each carbonate chemistry variable; and analyses that are commonly applied to carbonate chemistry information. Here, we quantify the uncertainties that are theoretically expected for measurements and calculations based on literature uncertainty estimates and that appear in practice in a large compilation of open-ocean carbonate chemistry measurements. We argue for the importance of quantifying both the random and systematic uncertainty contributions that collectively give rise to the combined uncertainties.

We propagate random and systematic contributions to uncertainty through carbonate chemistry calculations for the collection of measurements in the GLODAPv2.2022 data product, after removing secondary QC adjustments, and compare these propagated uncertainties to similar estimates obtained by comparing measured values with and calculated values from this data product. This analysis reveals:
  1. The variability in the residuals between measured and calculated carbonate chemistry variables is greater than we would expect from propagation of climate-quality measurement uncertainties. This implies that the measurements in the GLODAPv2.2022 data product (with or without adjustments) do not collectively meet the “climate-quality” standards.
  2. Some of this greater than expected discrepancy between measured and calculated carbonate chemistry variables could be due to measurements of pHT that predate the use of purified spectrophotometric indicator dyes, and we show that the subset of measurements of AT and CT in the GLODAPv.2022_unadjusted data product that are accompanied by spectrophotometric seawater pHT measurements are consistent with the climate-quality criteria (i.e., have r values ≤ 1 in Table 3). We find the subset of measurements with pHT obtained using purified spectrophotometric indicator dyes to have a particularly low random uncertainty estimate for pHT.
  3. The systematic offsets between measured and calculated carbonate chemistry values in this data product are consistent with systematic uncertainties inferred from literature estimates of uncertainties in both the thermodynamic carbonate chemistry constants and in the substance contents of non-carbonate molecules that contribute to seawater acid–base chemistry.
  4. The large uncertainties in carbonate chemistry constant sets, at present, prevent us from using inter-consistency calculations to assert that any one set of carbonate chemistry constants is superior to all others. However, this analysis supports several earlier constant set recommendations. We suggest (in Supporting Information Text S5) that exploration of correlations between uncertainties in constant values could be a productive topic of future research that might reduce propagated calculation uncertainty estimates.
  5. As García-Ibáñez et al. (2022) did before us, we show that the secondary QC adjustments applied to the GLODAPv2.2022 data product improve the consistency of the AT, CT, and pHT, but at the cost of making the seawater pHT measurements less consistent with the (relatively few) discrete measurements of seawater fCO2.

We contend that the overall uncertainty applicable to an analysis depends upon the input data and type of analysis (e.g., the number of distinct cruises that provided the data considered; whether measured or calculated values or both were used; and whether the analysis is concerned with overall values vs. differences regionally, over time, or from a reference value). We provide some guidelines for how a study can determine an appropriate uncertainty estimate based on the particulars of its analysis.

Data availability statement

The GLODAPv2.2022 data product is available at https://glodap.info/index.php/merged-and-adjusted-data-product-v2-2022/, with the associated adjustment table located at https://glodapv2-2022.geomar.de/. The metadata data product used to distinguish between various types of pH measurements is available as Supporting Information Materials for the companion paper (Carter et al. 2024).

Acknowledgments

The Ocean Carbonate System Intercomparison Forum (OCSIF, https://www.us-ocb.org/ocean-carbonate-system-intercomparison-forum/) is a working group of subject matter experts that was established in 2019 with support from the Ocean Carbon and Biogeochemistry (OCB, us-ocb.org) Project Office, which receives funding from the National Science Foundation (NSF OCE-1850983) and the National Aeronautics and Space Administration (NASA NNX17AB17G). This paper represents the compiled outcomes and discussions of OCSIF members over the past 3 yr. OCSIF has sole responsibility for the contents of this report and the questions, findings, and recommendations within. The views expressed in this report do not necessarily represent the views of the U.S. Department of Commerce or the National Institute of Standards and Technology. BRC thanks the Global Ocean Monitoring and Observing program of NOAA for funding the Carbon Data Management and Synthesis Program (Fund Ref. 100007298, program officer: Kathy Tedesco) and thereby supporting his involvement in OCSIF activities. JDS thanks the Global Ocean Monitoring and Observing program of NOAA (Award NA21OAR4310251), NOAA PMEL, and the University of Washington CICOES. RJW acknowledges the National Science Foundation Division of Ocean Sciences (Awards OCE-1923312 and OCE-2148468) and the MIT mTerra Catalyst Fund. KMS thanks NOAA AOML and the University of Miami CIMAS. AJF was supported by NOAA PMEL. MÁ thanks the IEO-CSIC internal project RADPROF. WJC, RAE, and XL thank NOAA's Ocean Acidification Program via award: NA17OAR0170332. The CICOES and PMEL contributions to this effort are numbers 2024-1348 and 5577, respectively. We thank the other members of the OCSIF working group and the community at large for helpful contributions and insights to our discussions and analyses, and thank the generations of global ocean ship-based discrete carbonate chemistry analysts and investigators who have contributed to the many cruises that were incorporated into the GLODAPv2 data product.

    Conflict of Interest

    The authors declare no conflicts of interest.