Characterizing Limits of Precision for Dissolved Organic Nitrogen

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Letter

Characterizing Limits of Precision for Dissolved Organic Nitrogen Calculations James F. Saunders, Yun Yu, James H. McCutchan, and Fernando L. Rosario-Ortiz Environ. Sci. Technol. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.estlett.7b00416 • Publication Date (Web): 09 Oct 2017 Downloaded from http://pubs.acs.org on October 11, 2017

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Environmental Science & Technology Letters

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Characterizing Limits of Precision for Dissolved Organic

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Nitrogen Calculations

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James F. Saunders, III†,*, Yun Yu†, James H. McCutchan, Jr†† and Fernando L. Rosario-

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Ortiz†,* †

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Department of Civil, Environmental and Architectural Engineering, University of Colorado, Boulder, CO 80309

††

Center for Limnology, Cooperative Institute for Research in Environmental Sciences,

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University of Colorado, Boulder, CO 80309

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* Corresponding Authors: [email protected]; (303)-906-0407;

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[email protected]; (303)-492-7607

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ACS Paragon Plus Environment

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ABSTRACT The usefulness of dissolved organic nitrogen (DON) data to environmental

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science depends on the precision of each calculated concentration. Precision of a

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calculated DON concentration is based on propagation of error from the measured

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nitrogen fractions used to calculate the DON concentration. We present an improved

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approach for calculating DON precision that strengthens conventional error propagation

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by developing empirical relationships between precision and concentration for each of

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the measured nitrogen fractions used to calculate DON concentration. Because the

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concentration and relative importance of each measured nitrogen fraction differs among

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samples, DON precision and the corresponding detection limit are likely to be different

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for each sample. Case studies from two different research efforts – a synoptic study of

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surface water DON and an experimental assessment of DON leached from heat-treated

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soils – demonstrate how the proposed approach can be tailored to the analytical methods

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and concentration ranges expected for any research project. In addition, current

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recommendations for pretreatment (e.g., dialysis) to improve DON precision should be

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modified to include consideration of analytical precision. Improved characterization of

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DON precision facilitates a realistic appraisal of sample-specific detection limits, and the

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results can be generalized to support decisions about pretreatment and statistical analysis

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of DON data.

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INTRODUCTION

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Quantification of dissolved organic nitrogen (DON) is important for basic and

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applied research in many disciplines, including atmospheric science, oceanography, and

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limnology.1-5 For example, DON enrichment raises concerns about eutrophication in

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estuaries,6 increasing levels of precursors for nitrogenous disinfection byproducts pose

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risks for drinking water treatment,7 and there is growing interest in the bioavailability of

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DON discharged by wastewater treatment facilities.8-9

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It is not practicable to measure DON concentrations either in aggregate or as the

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sum of its numerous and diverse components. The components of DON in aquatic

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systems may include proteins, humic-like substances, urea, peptides, amino sugars,

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purines, pyrimidines, pteridines, amides, methyl amides, and various other compounds.10

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Instead, it is common practice3, 11-14 to calculate DON concentration by measuring total

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dissolved nitrogen (TDN) and subtracting dissolved inorganic nitrogen (DIN), which is

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the sum of two or three fractions that are easily measured.

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Because DON concentrations are calculated and not directly measured, there is no

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direct method of assessing analytical precision. The precision problem for DON is not

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new and can be addressed with an error-propagation approach11 that accumulates the

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measurement errors contributed by each nitrogen fraction represented in the calculation

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of DON concentration. For example, when DIN is measured as three separate fractions

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(i.e., nitrate, nitrite, and ammonia), variance for the calculated DON concentration is the

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sum of variances for TDN, ammonia, nitrite, and nitrate. Consequently, the calculated

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DON concentration will be less precise, in absolute terms, than the measured TDN

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concentration.


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Precision has direct bearing on the problem of negative DON concentrations that

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appear frequently in the literature.15 If the true DON concentration in a sample is zero, for

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instance, it is reasonable to expect that half of the calculations from replicate analyses

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would yield small negative values and half would yield small positive values due to

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accumulation of error from the measured nitrogen fractions. Consistent application of the

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error-propagation approach to define DON precision and establish detection limits could

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do much to simplify reporting and avoid awkward decisions about re-coding16 or

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retaining17-18 negative values. Alternatively, it is possible to calculate DON precision and

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detection limits based on replicate measurements of the same sample,13 but the added cost

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of sufficient replication (e.g., 5 per sample) is rarely warranted.

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Previous efforts to estimate DON precision by the error-propagation approach

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have generally relied on one or the other of two common assumptions concerning the

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relationship between precision and concentration for the measured nitrogen fractions.

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One assumption holds that absolute precision (standard deviation) is constant and is

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independent of concentration, and the other assumption holds that relative precision

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(relative standard deviation) is constant and is a fixed proportion of concentration. Both

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assumptions have been applied in the literature (see SI Text S1 for examples).

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The assumption of constant relative precision is more common in the literature

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and has led to insights linking DON precision to the ratio of DIN concentration to TDN

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concentration. One such study found that DON precision diminished rapidly as the

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DIN/TDN ratio increased above 0.60 (i.e., DON less than 40% of TDN).14 Another study

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placed the threshold DIN/TDN ratio at about 0.85 (i.e., DON less than 15%).13 For cases

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where the threshold ratio is exceeded, both studies recommend dialysis pretreatment to


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improve DON precision. Dialysis, which lowers the DIN/TDN ratio by removing DIN

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but not DON, can improve DON precision, but only if reduction of DIN concentration

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yields a commensurate improvement in DIN precision.

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For direct measurements of nitrogen fractions, neither constant absolute precision

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nor constant relative precision alone is an appropriate assumption for all concentrations.

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However, both assumptions can be integrated appropriately by a two-component variance

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model, based on analytical experience.19-21 This variance model can be developed for the

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useful range of concentrations for each analytical method used to calculate DON

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concentrations (Figure 1, Text S2, Equations S1-S4). Evaluation of the two-component

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variance model shows why each of the two assumptions about precision will fail in the

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wrong part of the concentration spectrum. Assuming that precision is governed only by a

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constant standard deviation overestimates precision at high concentrations, and assuming

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that precision is governed only by a constant relative standard deviation (RSD)

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overestimates precision at low concentrations (Figure 1). Joining constant standard

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deviation with constant RSD in a two-component variance model yields a combined

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standard deviation, as shown over a range of concentrations in Figure 1. Proper

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characterization of DON precision, therefore, should rely on development of a two-

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component variance model for each of the measured nitrogen fractions.

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In this work, we take a fresh look at DON precision by improving the variance

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estimates that support implementation of the error-propagation approach. A two-

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component variance model is used to characterize empirical relationships between

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precision and concentration for each of the analytical methods supporting calculation of

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DON

concentration.

Characterization

of

sample-specific


precision

for

DON

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concentration will provide the detection limits necessary for statistical analysis, and it can

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help decide when pretreatment, such as dialysis, to reduce DIN is likely to improve DON

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precision.

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MATERIALS AND METHODS

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Samples of surface water and soil leachate were analyzed for nitrogen fractions by

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different methods, including the two most common TDN methods – persulfate oxidation

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and high-temperature catalytic oxidation. Surface water samples collected in and near

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Rocky Mountain National Park, Colorado, USA were analyzed for nitrate, nitrite,

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ammonia, and TDN. Soils from the Colorado Front Range, which were thermally altered

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and leached to simulate the effects of wildfires on nutrient release, were analyzed for

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nitrate+nitrite, ammonia, and TDN. Sample collection, processing and analytical methods

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are described in the Supporting Information (Text S3 and S4).

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For each analytical method, precision was characterized for a series of

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concentrations spanning the range expected for each set of samples. At each standard

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level, the standard deviation and the RSD were determined from replicate measurements

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of concentration. The RSD was calculated with the average measured concentration as

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the denominator, rather than the nominal standard concentration, because the average of

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measured values is “of the same metric” as the standard deviation.22 The DON

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concentration for a sample is considered below detection if the RSD for DON in that

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sample is greater than 1/3 (Text S2). Details of replicates, standards, and precision are

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presented in the SI (Text S3 and S4).


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The relationship between precision and concentration was determined empirically

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for each analytical method (Figures S2-S3). A region of constant standard deviation was

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generally evident, but the measured concentrations may or may not have included much

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of the region of constant RSD. Where the constant RSD could be defined, the two-

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component variance model was applied; where constant RSD could not be defined, a

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power function was used to describe the relationship between precision and concentration

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over the available analytical range (Tables S2 and S5). Ultimately, the aim is practical,

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rather than theoretical, and a defensible model must be tailored to each method.

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Precision of the calculated DON concentration is estimated with the error-

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propagation approach by applying concentration-specific characterizations of precision

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for each analytical method to each sample (sample calculations are given in Tables S3

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and S6). This approach can be applied to any combination of concentrations for the

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nitrogen fractions used to calculate the DON concentration, including cases where the

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measured value of a nitrogen fraction was below detection.

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RESULTS AND DISCUSSION

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Relationships between precision and concentration derived for each analytical

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method were used to calculate DON precision for each sample of surface water or soil

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leachate. Sample-specific calculations are required because the relative and absolute

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amounts of the inorganic fractions vary among the samples (Tables S3 and S6).

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Consequently, two samples with the same DON concentration could have different

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standard deviations.

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DON Precision in Surface Water Samples

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The error-propagation approach was used to derive a standard deviation and a

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detection limit for DON in each of 210 surface water samples. Even though high-

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precision analytical methods were used, 92 of 210 DON concentrations were below

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detection. A high proportion of non-detects may be common for surface waters,

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especially where anthropogenic influences are small.

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An association between precision and the DIN/TDN ratio is evident for the

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surface water samples, although it is more complex than has been reported in previous

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studies (Figure 2). For all samples with a DIN/TDN ratio less than about 0.6, DON

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concentrations exceeded the sample-specific detection limits. Conversely, for all samples

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with a DIN/TDN ratio greater than about 0.85, DON concentrations were below

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detection. That these ratios match ratios reported previously in the literature is

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misleading; as will be shown later, thresholds also depend on relative precision.

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The quantitative basis for calculating sample-specific DON precision developed

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in this study creates an opportunity to gain further insights regarding the potential

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benefits of pretreatment, such as dialysis, to improve DON precision by reducing DIN

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concentrations. In a hypothetical scenario based entirely on calculations, it is assumed

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that pretreatment removes 90% of the nitrate, which is reasonable for dialysis,15 and that

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dialysis does not alter the DON concentration. DON precision can be improved only

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when reducing concentrations of nitrate (and thus also TDN) also reduces the respective

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contributions of variance. The precision-concentration relationships developed in this

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study were used to calculate DON precision before and after hypothetical dialysis

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treatment (Table S3). Under this scenario, about half of the surface water samples (43 of

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92) that were initially below detection would have benefitted from pretreatment to reduce


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nitrate concentration; DON concentrations for the rest of the samples (49 of 92) would

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have remained below detection limit. The samples that might benefit, based on this

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hypothetical pretreatment scenario, occupy a relatively narrow band in the spectrum of

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DIN/TDN ratios, rising from about 0.6 at low TDN concentrations to more than 0.9 at

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high TDN concentrations (Figure 2).

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The foregoing analysis of surface water samples and exploration of the

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hypothetical pretreatment scenario illustrate the risk of relying on a single threshold for

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the DIN/TDN ratio as a criterion for pretreatment. Furthermore, the context provided by

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sample-specific detection limits shows that pretreatment will not always improve DON

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precision enough to be worthwhile; if precision cannot be improved to the point that the

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RSD is less than or equal to one-third of the DON concentration, pretreatment will not be

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worthwhile. These conclusions reflect the importance of careful characterization of the

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relationships between precision and concentration for all measured nitrogen fractions.

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DON Precision in Soil Leachate Samples

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Soil leachate samples, representing four replicates each of 5 treatments (i.e.,

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heating temperature) and a control set (unheated) of soils from six sites (Text S4), were

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analyzed for TDN and two inorganic nitrogen fractions – nitrate+nitrite and ammonia.

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DON concentrations were below detection in 24 of 144 samples, primarily those heated

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to 550 °C. The DON concentrations that were below detection are associated with low

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TDN concentrations where absolute precision is constant or relatively insensitive to

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changes in concentration. Consequently, pretreatment to reduce DIN in those samples


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probably would not be worthwhile because lowering the DIN concentrations would do

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little to improve DON precision.

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Predicting DON Precision

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The ability to generalize about opportunities to improve DON precision would be

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very useful. To some extent, improving analytical precision can help, although the real

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opportunities lie chiefly with the TDN method.13 Arguably more useful would be the

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ability to predict when pretreatment could be beneficial. Generalizing on the basis of

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published thresholds for the DIN/TDN ratio alone is of limited utility because those

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thresholds are not currently linked to analytical precision or calculated DON precision.

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There appears to be a strong connection between a threshold DIN/TDN ratio and the

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TDN concentration (Figure 2), suggesting that generalizations regarding DON precision

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must involve both the DIN/TDN ratio and TDN precision.

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Establishing a basis for predicting DON precision could help explain why

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previous studies have reached different conclusions about thresholds for the DIN/TDN

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ratio. In addition, when DON precision is framed in terms of a detection limit based on

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the RSD (the DON concentration is below detection if the RSD is greater than 1/3), it

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becomes possible to assess the need for, and potential benefit of, pretreatment. To

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simplify matters, the following explanation considers DIN concentration in aggregate

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(i.e., the sum of nitrite, nitrate, and ammonia), and with the understanding that DIN

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variance also is aggregated.

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DON precision can be cast in terms of TDN concentration and precision after an

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assumption is made regarding the variance of DIN relative to that of TDN. With

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commonly used analytical methods, the variance of the DIN fractions, even in aggregate,


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is typically much less than the variance of TDN measurements. In this study, DIN

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variance was typically only 1% of the TDN variance for surface water samples. When the

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contribution from DIN variance is negligible, the threshold for the DIN/TDN ratio, f, can

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be defined as follows (see Text S5 for derivation):

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݂ = 1 − 3 ∗ ܴܵ‫்ܦ‬஽ே

(Eq. 1)

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Equation 1 provides an upper bound for the threshold ratio because it assumes that

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DON precision is determined solely by TDN precision. Increasing the relative importance

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of DIN variance reduces the threshold ratio (Text S5). For example, in the soil leachate

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samples, the DIN variance was typically about 20% of the TDN variance. If the DIN

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variance is as much as 50% of the TDN variance, the equation would be as follows:

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݂ = 1 − 3.67 ∗ ܴܵ‫்ܦ‬஽ே

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The central role for the RSDTDN, which links TDN precision and concentration,

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can be highlighted by comparing the two analytical methods used in this study. For both

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of the TDN methods, the threshold DIN/TDN ratio is sensitive to TDN concentration,

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and it is clear that thresholds for the DIN/TDN ratio can be almost any number between

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zero and one (Figure 3). Thus, the two previously published thresholds (0.6 and 0.85) do

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not represent the universe of possibilities largely because they fail to incorporate

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analytical precision.

(Eq. 2)

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Two points made in this study contribute to a better understanding of DON

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precision. The first point is that the relationship between precision and concentration

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generally is more complicated than can be captured with a constant standard deviation or

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a constant RSD; a two-component variance model provides a more realistic foundation.

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The second point is that the relative precision of TDN measurements, which varies across


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the concentration spectrum, is the primary determinant of the threshold ratio. High

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relative precision for TDN, which is more likely at high concentration, makes it easier to

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resolve DON when the DIN/TDN ratio is high, irrespective of concentration.

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It should now be clear that no single threshold for the DIN/TDN ratio can be

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applied universally. The threshold(s) applicable in a particular study or for a particular set

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of samples will depend largely on the precision of the methods used to analyze those

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samples. If a single threshold is chosen, it should be justified on the basis of the methods

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used and samples analyzed in a particular study.

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Environmental Implications

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This study yields two unexpected observations related to the precision of DON

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concentrations, both of which are relevant to studies in environmental sciences. The first

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observation is the large number of surface water samples in which the DON was below

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detection despite having used high-precision analytical methods. It is difficult to know

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how common this problem might be in other studies because detection limits are rarely

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applied to DON concentrations reported in the literature. However, the numerous reports

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of negative values suggest that concentrations below detection are common. We

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recommend general use of a simple detection limit (RSDDON equal to 1/3) for DON

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concentration and encourage broader use of statistical techniques appropriate when

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censored data are present.23-24

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The second observation concerns expectations that pretreatment will necessarily

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yield better DON results. Many studies in the environmental sciences would benefit from

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better resolution for DON concentrations, and dialysis pretreatment has been shown to be

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helpful. However, pretreatment is not a panacea, because it does not always improve


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DON precision enough to be worthwhile. As shown above in the hypothetical scenario

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involving our surface water samples, about half of the candidate samples (i.e., those with

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DON concentration below detection without pretreatment) would have yielded a

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meaningful DON concentration (i.e., above detection) following pretreatment. Prediction

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of the success rate on the basis of a thorough characterization of precision-concentration

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relationships for the relevant analytical methods creates the basis for an informed

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decision about allocating resources to pretreatment measures intended to improve DON

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precision.

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ASSOCIATED CONTENT

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Supporting Information

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The Supporting Information is available free of charge on the ACS Publications website

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at __________. Additional method details, statistical analysis, and example calculations

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with figures and tables (PDF).

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ACKNOWLEDGMENTS

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The authors would like to acknowledge financial support from the National Science

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Foundation (CBET 1512705) and the National Oceanic and Atmospheric Administration

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Western Water Assessment Regional Integrated Sciences and Assessments program at

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the University of Colorado. Holly Miller at the Arikaree Environmental Laboratory, Ariel

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Retuta of the University of Colorado at Boulder, and Deborah Martin at the USGS

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provided assistance for the processing and analysis of soil samples. Cheri Yost and Paul

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McLaughlin (US National Park Service) provided logistical support for collection of


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surface water samples from Rocky Mountain National Park. We also thank two

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anonymous reviewers for helpful comments.

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REFERENCES

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(3) Letscher, R. T.; Hansell, D. A.; Carlson, C. A.; Lumpkin, R.; Knapp, A. N.

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Dissolved organic nitrogen in the global surface ocean: Distribution and fate. Global

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with ozone oxidation. Water Res. 2014, 54: 318-326.

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Atmos. Environ. 2003, 37, 2173-2191.

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Optimization of dissolved organic nitrogen (DON) measurements in aqueous samples

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with high inorganic nitrogen concentrations. Sci. Total Environ. 2007, 386, 103-113.

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(22) Proctor, C. H. A simple definition of detection limit. J. Agric. Biol. Environ. Stat. 2008, 13, 1-23. (23) Helsel, D. Nondetects and Data Analysis: Statistics for Censored Environmental Data, 2nd ed.; John Wiley and Sons: New York, NY, 2012. (24) Haslauer, C. P.; Meyer, J. R.; Bardossy, A.; Parker, B. L. Estimating a

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7510.

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FIGURES

Standard μg/L Standard Deviation, Deviation, μg/L

100 100 Absolute Absolute Relative Relative

10 10

Combined Combined 11

0.1 0.1

0.01 0.01 11

10 10 100 Concentration, Concentration, μg/L μg/L

1000 1000

356 357

Figure 1. Characterization of analytical precision for a range of nitrate-nitrogen

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concentrations based on the two-component variance model explained in the text. The

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model joins a component of constant absolute precision (Absolute) and a component of

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constant relative precision (Relative) to yield a concentration-specific combined standard

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deviation (Combined).

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120%

DIN as % of TDN

100% 80% 60% 40% 20% 0% 10

Pretreatment Benefit

100 TDN, μg/L No Pretreatment Benefit

1000

DON Detectable

363 364

Figure 2. Surface water samples classified according to potential benefit from

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pretreatment. DON was detectable without pretreatment in 118 samples and below

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detection in the other 92. Pretreatment under the hypothetical scenario described in the

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text could have provided benefit in 43 samples, and the DON concentration would have

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remained below detection in the other 49 samples.

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Threshold DIN/TDN Ratio

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1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0

Center Arikaree

10

100

1000

10000

TDN, μg/L 370 371

Figure 3. Threshold values for the DIN/TDN ratio based on analytical results obtained by

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the Center for Limnology Lab (persulfate oxidation) and the Arikaree Lab (high-

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temperature catalytic oxidation). Thresholds are calculated using Equation 1, which

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assumes that variance for the inorganic fraction is negligible compared to that of TDN.

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The dashed lines show detection limits for each method.

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Total Dissolved Nitrogen

0

100

200

300

400

500

Dissolved Inorganic Nitrogen

0

100

200

300

400

500

Dissolved Organic Nitrogen, by subtraction

0

100

200

300

400

500

Concentration

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20

Page 21 Environmental of 21 Science & Technology Letters

Total Dissolved Nitrogen

0

100

200

300

400

500

Dissolved Inorganic Nitrogen

0

100

200

300

400

500

Dissolved Organic Nitrogen, by subtraction

0


100

200

300

Concentration

400

500

Characterizing Limits of Precision for Dissolved Organic Nitrogen

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