dataesr/scientific-paragraphs-categorization huggingface dataset:
With the common goal of more accurately and consistently quantifying ambient concentrations of free metal ions and natural organic ligands in aquatic ecosystems, researchers from 15 laboratories that routinely analyze trace metal speciation participated in an intercomparison of statistical methods used to model their most common type of experimental dataset, the complexometric titration. All were asked to apply statistical techniques that they were familiar with to model synthetic titration data that are typical of those obtained by applying stateof-the-art electrochemical methodsanodic stripping voltammetry (ASV) and competitive ligand equilibration-adsorptive cathodic stripping voltammetry (CLE-ACSV)to the analysis of natural waters. Herein, we compare their estimates for parameters describing the natural ligands, examine the accuracy of inferred ambient free metal ion concentrations ([M f ]), and evaluate the influence of the various methods and assumptions used on these results.
The root-meansquared relative error between the fitted observations and the simulated curves should be comparable to the expected precision of the analytical method and upon visual inspection the distribution of residuals should not be skewed. Modeling the synthetic, CLE-ACSV-type titration dataset, which comprises 5 titration curves generated at different analytical windows or levels of competing ligand added to the virtual sample, proved to be more challenging due to the random measurement error that was incorporated. Comparison of the submitted results was complicated by the participants' differing interpretations of their task. Most adopted the provided 'true' instrumental sensitivity in modeling the CLE-ACSV curves, but several estimated sensitivities using internal calibration, exactly as is required for actual samples.
Close inspection of the biases and variability in the estimates of ligand parameters and in predictions of ambient [M f ] revealed that the best results were obtained by the direct approach. Linear regression of transformed data yielded the largest bias and greatest variability, while non-linear isotherm fitting generated results with mean bias comparable to direct modeling, but also with greater variability. Participants that performed a unified analysis of ACSV titration curves at multiple detection windows for a sample improved their results regardless of the basic mathematical approach taken. Overall, the three most accurate sets of results were obtained using direct modeling of the unified multiwindow dataset, while the single most accurate set of results also included simultaneous calibration.
We therefore recommend that where sample volume and time permit, titration experiments for all natural water samples be designed to include two or more detection windows, especially for coastal and estuarine waters. It is vital that more practical experimental designs for multi-window titrations be developed. Finally, while all mathematical approaches proved to be adequate for some datasets, matrix-based equilibrium models proved to be most naturally suited for the most challenging cases encountered in this work, i. e. , experiments where the added ligand in ACSV became titrated. The ProMCC program  (Omanović et al. , this issue)  as well as the Excel Add-in based KINETEQL Multiwindow Solver spreadsheet  (Hudson, 2014)  have this capability and have been made available for public use as a result of this intercomparison exercise.
The complete mass balance for M in a natural water is then given by: M ½ T ¼ ΣML ½ þ M 0 Â Ã ð7Þ where  [ΣML]  is the total concentration of metal bound by all classes of natural organic ligands. The basic equationsequilibrium mass laws and mass balancesunderlying this speciation model are essentially the same across the numerous papers where they have been developed more fully, e. g. ,  van den Berg (1982a) ,  Ružić (1982) ,  Cabaniss and Shuman (1988) ,  Miller and Bruland (1997) , and  Wells et al. (2013). Available programs: XLS: Excel spreadsheets -VDB (van den Berg, 2014), KMS  (Hudson, 2014) ; NLR: Non-linear regression codes written for various software packages -G/R  (Gerringa et al. , 2014) ,  Hudson et al. (2003) ,  Laglera et al. (2013) ,  Sander et al. (2011) ; Stand-alone programs -FITEQL:  Westall (1982) ; PROSECE: While the nomenclature these papers employ is also fairly consistent, the symbols used for key variables are not.
Ψ M , 'modeling' approach in Table  1 ). Shuman and Woodward (1973)  took this approach using the analytical solution to a one-ligand model. McKnight et al. (1983)  directly modeled ISE titrations using the FITEQL program  (Westall, 1982) , which numerically solves a complete speciation model. ACSV titrations have been directly modeled by  Voelker and Kogut (2001)  and  Kogut and Voelker (2003)  who also used FITEQL, and by  Garnier et al. (2004a,b) , who employed the PROSECE model. However, these works all retain the conceptual separation, or decoupling, of speciation modeling from calibration.
Bruland et al. (2000)  assigned this variation to differences in analytical competition strengths (detection windows) of the methods used, noting that with increasing detection window [L i ] T values decreased, while K i increased. Buck et al. (2012a)  concluded that consensus between different labs could be attained when using the same analytical method at the same α′, but inconsistencies were found for Fe between titrations with different added ligands. Recommendations arising from this inter-calibration were that: 1) a multi-detection window titrations would probably help better characterize the natural Cu-binding ligands in open ocean waters, and 2) all researchers should agree to use at least one 'standard' detection window to facilitate intercomparison of results between groups. In both cases, it became clear that along with refining analytical methods, achieving the goal of mutually-consistent complexation datasets requires a coherent strategy in choosing analytical detection windows, with multiple window titrations emerging as an important tool.
3 ), it is in fact more appropriate to analyze multiwindow titrations as a single dataset than as individual curves. What made it possible to constrain S max at the same time was the requirement that the same ligand parameters describe complexation in all detection windows. This validity of this 'criterion of coherence' was confirmed by improved fits and lower parameter uncertainties for models of the multiwindow datasets generated in the  Bruland et al. (2000)  intercomparison, especially Moffett's ACSV titrations using bzac. It also became clear that the large uncertainty inherent in analyzing any single curve meant that it was in no way justified to conclude that differences in ligand parameters obtained by fitting curves at different α′ necessarily meant that different ligand classes were detected.
In three different datasets, no more than 2 distinct classes could be fitted when simultaneously analyzing 5 distinct windows for each sample  (Hudson et al. , 2003). These insights were confirmed by implementing the unified multiwindow approach using a matrixbased equilibrium model  (Sander et al. , 2011). A subsequent development in design of titration experiments derived from the unified multiwindow approach is the 'reverse titration,' which aims at quantifying very strong ligands present at concentrations lower than ambient [M] T. Rather than titrating ligands by adding metals, as in a 'forward' titration, Nuester and van den Berg (2005) systematically increased [AL] T and analyzed the I p data in a unified manner, despite the fact that each point differed in α CuSAx (see also  Hawkes et al.
, 2012b). This intercomparison expands upon previous efforts to intercalibrate analytical methods by examining outcomes from participants' modeling of synthetic datasets that are similar to routinely generated ASV-and ACSV-type complexometric titrations. Participants from 15 different laboratories applied the data analysis tools that each routinely employ and submitted their interpretations of the data. Here, we report these results and compare them to the 'correct' values of ligand parameters and to [M f ] predicted at both low and high ambient [M] T.
Generation of synthetic datasets Synthetic datasets representing complexometric titrations of organic, metal-binding ligands naturally-present in surface waters were generated by S. G. S. and I. P. using equilibrium speciation models plus the above equations relating I p , [M meas ], and R AL. Each virtual sample is defined by a set of 'true' parameters (Table  2 ) describing the natural ligands present, i. e. , their concentrations ([L i ] T ) and complex stability constants (K i ). The reagent additions made in each titration and the simulated instrumental response mimic complexometric analysis of real samples by either ASV or CLE-ACSV. All complete sets of synthetic data are available in Appendix 1.
ASV-type, single detection window datasets The ASV-type, single-detection window (SW) datasets provided to the participants were all noise-free. 'Samples' A-C contained just a single ligand class and were titrated using linear-, logarithmic-and decadal-distributions of metal additions, resulting in 9 individual titration curves (Table  2 ). Samples D-F contained 2 ligand classes each and were titrated using the same 3 distributions of metal additions, resulting in 9 additional titration datasets. The final ASV-type titration was generated for a sample (G) with 3 ligand classes. For samples A-F, participants were directed to choose a one-or twoligand model, as they deemed appropriate. For dataset G, participants were advised to include between 2 and 4 ligand classes. The former primarily tested participants' ability to accurately estimate complexation model parameters, while dataset G tested their ability to detect the presence of more than 2 ligand classes in a sample.
CLE-ACSV-type, multi-detection window datasets ACSV-type, multi-detection window (MW) titration datasets were generated for two different 'samples' containing two natural ligand classes each (Table  2 ). The first sample (dataset MW1) represented the more common case where [L 1 ] T b [L 2 ] T. The second sample (datasets MW2 and MW3) was designed to make L 2 difficult to detect since [L 2 ] T b [L 1 ] T. Titrations were generated for 5 different concentrations of added salicylaldoxime between 0. 5 and 70 μM. Random measurement error (noise) was added to the synthetic I p data in MW1 and MW3, while set MW2 was noise-free. Noise having both a proportional component of random error that averages 3% of the signal and a constant component was generated based on data from real Cu-SA titrations at the University of Otago  (Sander et al.
Instructions to participants Each participant received a package of data and instructions via email (See SCOR Working Group 139, 2014). For each simulated titration, participants were provided with experimental details, including the actual sensitivity (S for ASV and S max for ACSV) used to generate the synthetic voltammetric data and all values of independent and dependent variables for each point in the titration curve (I p , [M] T , and [AL] T if present). Other information needed for complexation modeling, including conditional stability constants for MAL x complexes, α 0 MALx for each detection window, and α M ′ were also provided. Participants were instructed to analyze each SW or MW dataset as if it were from a real sample and report the parameters for each ligand class, along with the number of ligand classes detected.
For the MW titrations, the directions also suggested that participants who lacked a modeling tool for analyzing the unified multiwindow dataset should fit the curves separately and decide whether the parameters were reliable or outside the detection window. The participants were asked to describe their methods of data analysis according to the scheme of Fig. 1. In order to gain deeper insights into other attributes needed to evaluate and compare the results, the participants were asked whether they i) removed some data points before fitting; ii) plotted original data (linear-linear, log-log or both); iii) transformed data according to VDBR, Scatchard, or LG methods or examined the same curve with more than one transformation; iv) used linear, nonlinear or both fitting methods, and if nonlinear, how they obtained initial guess parameters; and v) simulated or 'back calculated' the titration curve using their fitted parameters ([L i ] T , log K i ) in order to visually inspect the success of fitting.
Participants' methods and results In response to this intercomparison exercise, 15 participants reported 21 independent sets of results, which are referred to herein as the responses of participants a to w (Appendix 2), and described the methods they used to analyze the data (Appendix 3). All results have been categorized according to the methods of data analysis used (cf. Table  1 ). Unexpectedly, 8 of the 21 responses reported that the sensitivity S had been fitted or adjusted for at least some curves, meaning that the provided correct S values had been overlooked. Since S is never known a priori for a real dataset, it could be said that these participants treated the synthetic data exactly as one must treat real data. The importance of this distinction between those that adjusted S and those that did not should be apparent from the discussion of calibration above.
Evaluation of results Three basic metrics of the quality of participants' results are used herein. The first measures the quality of the fit to the data, while the second measures the accuracy of a parameter estimate. The third metric is the deviation of pM at particular [M] T of interest predicted from a particular parameter set from the value defined by the 'correct' ligand parameters. To assess the quality of fit to the observed titration curve of any given parameter set, all data points of the relevant titration curve were first simulated (I p calc ) for the reported parameter set and specified  [Cu]  T and [AL] T (see Fig. 1 ) using the program ProMCC  (Omanović et al. , in this issue). Two metrics of fit to the titration curve were then derived: RMSEF and RMS-RE. Note that these metrics may differ from the objective function optimized by participants.
Sources of error in parameter estimates An important complication in the MW1 dataset became apparent during the analysis of submitted results, namely that in the 3 MW1 titration curves with the lowest [SA] T added, α CuSAx was reduced by 11-61% by the end of the titration (Table  3 ). Consequently, the assumption that α′ remains fixed within a titration curve, which was made by all but 3 participants, was not consistent with the speciation model used to generate the synthetic data. Since less than 10% of data points are affected significantly and fits to the data were reasonably accurate with fixed α′ assumed, the problem went largely unnoticed by participants. Real ACSV titrations performed at low [AL] T may also be affected by this problem  (Kogut and Voelker, 2001) , albeit generally less than in our window MW1-1.
In order to derive 'correct' parameters for the speciation model with fixed α′, we fitted a set of ligand parameters to all five noise-free curves of MW1 both singly (Table  3 ) and simultaneously (Table  2 ). Herein, the simultaneously fitted set of parameters is referred to as the 'correct' parameters of the 'alternate' or 'fixed α′' model. Note that only the resultant L 2 parameters are noticeably different from the original model. Calculated [Cu f ] at 5 and 50 nM differs by less than 1%. The residuals of the MW1 data points from the alternate model are distributed similarly to those of the original model. N. B. The alternate parameters were derived solely for the purpose of evaluating responses in this comparison. This approach should not be used as an alternate means of analyzing real data.
Models and programs A variety of custom programs and commercial software packages were employed in this work. The synthetic data were generated using custom equilibrium speciation modeling software based on Morel Tablature  (Sander et al. , 2011). Much of the basic data manipulation was accomplished in Microsoft Excel, while specialized statistical analysis was performed using SAS v 9. 4 (SAS Systems). ProMCC  (Omanović et al. , in this issue)  was used to perform VDBR and LG fits of titration curves. Speciation calculations for graphs and evaluation of model error were performed using PROSECE (Programme d'Optimisation et de SpEciation Chimique dans l'Environnement)  (Garnier et al. , 2004a; Louis et al. , 2009)  and KINETEQL Multiwindow Solver  (Hudson, 2014). Software used by the participants is described in Appendix 3.
Of course, taking steps to correct poor model fits is crucial. Since non-linear fitting depends on initial guesses, it may suffice to choose an alternate initial guess and re-estimate ligand parameters. Removal of data points, which quite a few participants reported doing for the MW1 dataset, should not be undertaken just to improve model fit since doing so indulges confirmation bias. Statistical tests proving that a given point is truly an outlier are available and should be applied if data are suspect  (Miller, 1993).
Taken together these results suggest that the success of calibration, which in real samples dictates that the analyst estimate a value of S from the titration data, is fundamental to the success of the modeling effort. While the goal of internal calibration is to obtain an accurate sensitivity that accounts for surfactants present in the sample matrix, to the extent that any slope obtained by internal calibration is biased by untitrated weak ligands, the chances of detecting L 2 will also be reduced. This in turn increases the error in both pCu5 and pCu50 and propagates error into estimates of the L 2 parameters. Thus, the responses with calibrated slope provide us with a scenario closer to real-life, i. e. , where S is truly unknown and its estimate is biased low. Responses based on adopting the known S = R AL provide us with a less realistic scenario, but a better dataset for comparing methods of estimating parameter values.
In contrast, the log KL 2 of the Ψ FR2 N approach had a non-significant mean bias and mostly fell close to the ideal pCu50-logKL 2 line on Fig. 4   ) only spanned a range in [L 2 ] T from 173 to 233 nM. Upon close examination of the data using ProMCC software, we found that the systematic low bias resulted in large part from the peculiarities of these noised data on the fixed α′ models. Finally, we conclude our discussion of approaches that used S = R AL by noting that the lowest bias was exhibited by the two responses applying direct modeling (Ψ M ). The mean bias for response c) (Ψ VR2 M ) was non-significant for all parameters, with essentially exact means for [L 2 ] T of 153 nM and K 2 of 10 9. 91 M -1. Since it employed the fixed α′ model, response z′ was not quite as accurate, but it did yield tightly clustered parameters and predictions (Fig.
Effects of adjusting S on estimates of ligand parameters The calibration of S, while widely known to be problematic, has effects that remain poorly understood. For a two-ligand model, the error of fit weakly depends on S (Fig. 9 ). For example, for MW1-1, the noisy data causes fits to have a barely perceptible minimum at S max = 1. 083, while the fit to window MW1-3 has a minimum at S max = 0. 89. Thus, realistic confidence limits (CL) on S when fitted to individual curves must be at least ±0. 1 or so for the MW1 data. When combined with the already substantial CL generated by the fitting software for each parameter at fixed S, the uncertainty in S leads to even larger CL for the parameters. The difficulty that nonlinear regression software can have in converging for a two-ligand model applied to curves like the MW1 titrations reflects interactions of S and ligand parameters.
Visual inspection of data and simulation (back calculation) of titration curves While to this point, the focus has been on effects of calibration, we now consider an important aspect of the art of analyzing titration curves using non-linear regression tools, namely deriving initial guesses and recursively improving fits. To this end, we examine the data of the intermediate MW1-3 window ([SA] = 1. 9 μM) and the characteristic parameter estimates of six different participants (Fig. 10A to D ). In addition to plotting the back-calculated titration curves and given data (Fig. 10A ), we used the reported parameters to generate points that were then transformed into LG, VDBR, and Scatchard plots using ProMCC software  (Omanović et al. , in this issue). Looking at the curves in Fig. 10A , all but one result seems to have successfully fitted the data points.
Unified analysis of multiple window datasets When fitting a single titration curve, neither simple internal calibration (Table  3 ) nor fully coupled calibration/direct modeling (Fig. 9 ) can guarantee accurate estimates of S. However, by considering even two curves with distinct α′ simultaneously, the composite error function develops a distinct minimum near the correct slope (Fig. 9A ). With more windows, the minimum becomes even better defined and the uncertainties in model parameters greatly diminished  (Hudson, et al. , 2003; Sander et al. , 2011). Using the 5 windows of the MW1 dataset, participant t applied simultaneous calibration/modeling to obtain an S max that is correct to within 0. 01%, estimates of all ligand parameters that are effectively exact, and a mean fitting error (RMS-RE = 3.
Participant b also showed the value of this criterion even when performed manually. By averaging the best-fitting single window results, b obtained a very good overall fit to the complete dataset (RMS-RE = 4. 0%). Analyzing single titration curves when S max is not known is more challenging, however. Biased calibrations can be identified as suspect by visual inspection of speciation data on [Cu f ]-[Cu natural ] plots (Fig. 11B ). These transformations of MW1 data made using biased S ic values (Table  3 ) obviously lack coherence between windows, especially at the upper end of each curve. The estimated ligand parameters also yield widely disparate curves for [Cu f ] as a function of [Cu natural ]. None of the participants that modeled single curves with calibrated S reported unified parameters for MW1.
As discussed above, participant t was able to successfully calibrate S max by directly modeling the MW1 data in a unified fashion. This approach yields the simplest possible model that explains all of the data in a coherent manner, as is evident from the [Cu f ]-[Cu natural ] plot (Fig. 11C ). Two other participants, c and d, also employed direct modeling, but without simultaneous calibration, instead accepting the given S max of 1. The accuracy of their ligand parameter estimates and the very close fit to the titration data (RMS-RE = 3. 14 and 3. 16% respectively) confirm that the criterion of coherence between analytical windows is powerful and that direct modeling of multiple windows is potentially very accurate. In summary, only 6 of the 15 participating laboratories, plus two pseudo-participants, reported results for a unified analysis of the five MW1 titrations.
In all cases, they yielded very good to excellent predictions of pCu5 and pCu50 and ligand parameters (Fig. 7 ; Table  6 ), despite the inclusion of the problematical data from window MW1-5. Consider the example of participant c, whose pCu50 is more than a log unit high when calculated from window 5 alone (Fig. 7 ), but within 0. 01 log units of the correct value based on the unified analysis performed on windows 1-5. Participants b, h, y′, and z′ also had poor predictions for window 5, but quite good predictions for the unified datasets. The implied robustness of the unified multiwindow approach is heartening, since it suggests that even including single titration curves that are very difficult to interpret can be useful. While one would not intentionally design experiments to generate such data, it is helpful to know that it is not necessary to exclude such portions of a dataset and thereby run the risk of introducing confirmation bias.