Optimization of River Sampling: Application to Nutrients Distribution in

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Optimization of river sampling: application to nutrients distribution in Tagus river estuary Carlos Borges, Carla Palma, and Ricardo J. N. Bettencourt da Silva Anal. Chem., Just Accepted Manuscript • DOI: 10.1021/acs.analchem.8b05781 • Publication Date (Web): 08 Apr 2019 Downloaded from http://pubs.acs.org on April 16, 2019

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Analytical Chemistry

Optimization of river sampling: application to nutrients distribution in Tagus river estuary Carlos Borges†, Carla Palma†, Ricardo Bettencourt da Silva‡* †Instituto

Hidrográfico; R. Trinas 49, 1200-615 Lisboa, Portugal de Química Estrutural – Faculdade de Ciências da Universidade de Lisboa; Edifício C8, Campo Grande, 1749016 Lisboa, Portugal * E-mail: [email protected] ‡Centro

ABSTRACT: The assessment of river water pollution trends is affected by the seasonal variation of river conditions, the variability of pollution sources, the heterogeneity of pollutants distribution, the representativeness/uncertainty of sampling and the uncertainty of sample analysis. This work presents a methodology to model the uncertainty of river water sampling based on available information about the spatial distribution of the studied parameter in the river. It was studied the uncertainty from Single Sampling (SS) or by producing a composite sample by mixing m subsamples collected randomly (RS) or in a line that crosses the sampling circle (LS). This methodology was applied to the determination of nutrients (NOx, NO2, PO4 and SiO2) in an area of the Tagus river estuary with a range of about 350 m. This methodology can be applied to the determination of the mean value of other parameters in other river areas requiring a previous study of system heterogeneity. The spatial distribution of nutrients in the studied river area was characterized from the analysis of 10 samples collected at known geographical coordinates. The system heterogeneity was described by a 3D (x, y, z) surface with x and y variables for samples positions and z variable representing the measured nutrient levels. The randomization of this surface for the uncertainty of coordinates and repeatability of nutrient concentration measurement, using Monte Carlo simulations, allowed estimating the uncertainty of the three sampling strategies: SS, RS and LS. The uncertainty from RS and LS is equivalent and significantly smaller than from SS when at least three subsamples are mixed in the composite sample. The sampling relative standard uncertainty ranged from 0.31 % to 4.4 % producing nutrient concentration estimates in the river area with a relative expanded uncertainty of 5.9 % to 10 % for approximately 95 % confidence level (coverage factor of 2). The used spreadsheet is available as Supporting Information. The monitoring of the evolution of river water status is used to assess the adequacy of environmental protection policies such as maximum values set for the volume and concentration of nutrients and/or pollutants of wastewaters emissions. Standards and guidelines have been published for the in-situ determination of river water parameters or for the collection and preservation of samples that can be analyzed in the laboratory1-7. Some authors also studied the impact of river composition heterogeneity in the characterization of a sampling point8-11. However, when trends of river water composition need to be monitored, it is necessary to characterize a large river area since is more robust to river’s heterogeneity and representative of its status. This area would be characterized by the parameter value that would be obtained after mixing and analyzing the water of the river area that is equivalent to the mean of parameter values determined in the area. The estimated value of a river water parameter can only be compared with an estimate performed on another occasion or location if both values are reported with uncertainty. The measured value and its uncertainty define a confidence interval that encompasses the conventional true value of the measured quantity (i.e. the measurand) with a known probability, typically 95 % or 99 %12-14. Therefore, the measurement uncertainty must account for all systematic and random effects that affect the difference between the measured and the conventional true value, i.e. the measurement error12. The term quantity (symbol, q) is used in metrology for a quantitative parameter such as mass concentration (γ, mg L-1), molar concentration (c, mol L-1), mass fraction (w, mg kg-1) or pH12. In this work, the term quantity is used whenever concepts are applicable to different types of quantities. The uncertainty associated with the estimated value of a parameter in a river water area can be divided into sampling and sample analysis components. If a minimum variation of a water parameter in a river area needs to be detected, frequently, sampling and sample analysis must be optimized to guarantee that measurement uncertainty is small enough for the intended use of the monitoring15,16. This work quantifies the reduction of the sampling uncertainty by increasing the number of subsamples mixed in a composite sample subsequently analyzed to characterize the river water in a specific area, depth and time. The uncertainty of the analysis of the river water defines the minimum difference of the studied parameter that can be distinguished over time or in different locations. THEORY The spatial distribution of a river water parameter, at a specific depth, depends on river dimensions, topography, water flow, and the location and characteristics of the emission/pollution sources. If the major pollution source is the flow of a wastewater, it can contribute more to system heterogeneity than if the major pollution comes from air emissions. ACS Paragon Plus Environment

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After describing the spatial variation of the parameter in a river area, designated “sampling circle”, it is possible to model the variation of the sampling uncertainty with the sampling parameters. The sampling parameters are the number and distance of subsamples used to prepare a composite sample. The sampling uncertainty models can be used to define the minimum resources necessary to achieve the required sampling uncertainty. The spatial variation of the parameter in the sampling circle can produce not normally distributed parameter values of samples randomly collected inside the sampling circle. However, the distribution of composite samples values tend to become normally distributed as the number of subsamples mixed in the composite sample increases; this shift to normality is described by the Central Limit Theorem. To make sampling modelling feasible, it is necessary to define pragmatic ways of inferring about system heterogeneity from the collection of a limited number of samples with flexible geographic coordinates. It is difficult to sample the water from a river in predefined strict coordinates. The worst-case description of system heterogeneity can be used to reduce the chance of overestimating the sample representativeness (i.e. assuming that the sample is more representative than in fact is). The model of the spatial variation of the river water composition will be more accurate if more data about system heterogeneity are collected. Modelling and requirements for river sampling This section is divided in modelling and requirements definition for river sampling having in mind the purpose of the monitoring. Experimental Procedure The determination of the spatial variation of a river water parameter involves analyzing n samples collected at a specific depth and known coordinates in the sampling circle. The samplings should be performed at a distance not smaller than ten times the error/uncertainty of the GPS coordinates to avoid spending resources in characterizing indistinguishable positions. The coordinates are referenced to a conventional position close to the sampling circle, designated “ground”, to convert coordinates in longitudinal and latitudinal distances to the ground. In river areas where the flow is affected by the tide, samplings are performed at the stand of the tide when the stream and the tide are near equilibrium and the system’s dynamics reach its minimum. Samples are analyzed in repeatability conditions (i.e. in the same day; not necessarily the day of the sampling) within a time frame where the studied parameter is stable. Several documents1-3 describe the type of containers and the preservation conditions and time for many water parameters (See Experimental). Measurement repeatability Since the results dispersion of water samples analysis comes from the combination of intrinsic between samples parameter variability and measurement repeatability, it is necessary to quantify the standard deviation of measurement repeatability, 𝑠r. The 𝑠r can be estimated by the mean range, 𝐴, of duplicate results of the analysis of various thoroughly mixed river water samples since there is a known statistical relationship between these parameters: 𝑠r = 𝐴 1.12817. A range, 𝐴, of duplicate results is the absolute value of their difference. Duplicate results of the analysis of a homogeneous sample are accepted, for 95 % confidence level, if 𝐴 is not larger than the repeatability limit (2.8𝑠r) (𝐴 ≤ 2.8𝑠r)17. The 𝑠r is independent of the between samples variability but can vary with the parameter value. Alternatively, the 𝑠r can be estimated by the replicate analysis of each sample collected in the sampling circle by extracting the measurement repeatability from an analysis of variance18. The estimated 𝐴 of samples from different origins is divided in two quantity intervals: Interval I, between the Limit of Detection, LOD, 𝑞LOD, and two times the Limit of Quantification, LOQ, 2𝑞LOQ (i.e. [𝑞LOD; 2𝑞LOQ [), and Interval II, between 2𝑞LOQ and the maximum quantity of procedure validation, 𝑞𝑀𝑎𝑥 (i.e. [2𝑞LOQ, 𝑞𝑀𝑎𝑥[). Acronyms and symbols are presented in roman and italic, respectively; for instance, the acronym LOD and the value of this limit 𝑞LOD. This division in two quantity intervals results from the fact that 𝑠r is constant below 2𝑞LOQ and 𝑠′r (𝑠′r = 𝑠r 𝑞; the apostrophes identifies relative values) is approximately constant above 2𝑞LOQ regardless of the parameter15,16,19,20. For Interval I, 𝑠r〈I〉 = 𝐴〈I〉 1.128, where 〈I〉 identifies the interval, and for Interval II, the 𝑠′r〈II〉 = 𝐴′〈II〉 1.128 where the relative range 𝐴 ′=𝐴 𝑞 and 𝑞 is the mean of duplicate results. Water parameter heterogeneity Assuming the value of the studied parameter/quantity in the sampling circle has a normal distribution, its dispersion can be quantified by the standard deviation, 𝑠, of results of the analysis of n samples collected in the sampling circle. Therefore, the standard deviation, 𝑠S, that quantifies the intrinsic variability of the quantity in the river water samples, independent of 𝑠r, is estimated by eq 1. The 𝑠S is the sampling uncertainty evaluated from n sample results. (1) 𝑠S = 𝑠2 ― 𝑠2r ACS Paragon Plus Environment

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where 𝑠r will be equal to 𝑠r〈I〉 or 𝑞SC𝑠′r〈II〉 for a mean quantity, 𝑞SC , in the sampling circle (“SC”) within Interval I or Interval II, respectively. When the spatial distribution of the quantity is heterogeneous, the standard deviation of sample results can underestimate the complexity of the system. Water parameter spatial variation The assessment of the spatial variation of the studied quantity in the sampling circle depends on the number of sampled points, their relative positioning and the measured values of the samples. This evaluation is also affected by the uncertainty associated with the coordinates and measured quantities in samples, and impacts on the estimated mean value of the quantity in the circle. A modelling strategy to quantify the impact of all these factors on the estimated mean was developed. The information collected at each sampling point i (i = 1 to n) is described by three variables: xi and yi for the longitudinal and latitudinal distance to the ‘ground’, and zi for the measured quantity. The n points (x, y, z) are used to build a 3D surface where segments are used to connect the closest neighbour points producing multiple triangular surfaces with different shapes and sizes. Figure 1 represents an example of such a surface for nitrite concentration in an area of the Tagus River estuary. This surface is subsequently randomized many, l, times by changing the values of points variables given the uncertainty of xi, yi and zi (illustrated by the zoom of one point of Figure 1). The simulated surface variability represents the uncertainty of the spatial variability model of the water parameter and is used to estimate the uncertainty of different sampling types. Single sampling uncertainty For each simulated 3D surface (x, y, z), longitudinal and latitudinal distances to the ground (xh, yh) are randomly selected and their water parameter, zh, estimated by projecting (xh, yh) on the surface (see Figure 1). The standard deviation of l simulated zh, that scan the sampling circle, quantifies the standard deviation, 𝑠(SS), of measured quantity values inside the sampling circle (the acronym SS stands for ”Single Sampling”). The numerical determination of 𝑠(SS) is designated a Monte Carlo Method. The stages of zh simulation are described in section 1 of the Supporting Information. If 𝑠r is subtracted to 𝑠(SS), as described in eq 1, the single sampling uncertainty, 𝑠S(SS), is estimated from a more informed knowledge about the spatial variability of the parameter than the standard deviation of n sample results. If the distribution of simulated zh deviates significantly from normality, their dispersion should not be described by 𝑠(SS) . In that case, the complex distribution of zh or other distribution models must be considered. Random composite sampling uncertainty A random composite sampling (RS) involves collecting m subsamples in positions randomly selected inside the sampling circle and mixing subsamples in the same container to produce a composite sample. The standard uncertainty of random composite sampling, 𝑠S(RS;𝑚) is estimated by eq 2 from 𝑠S(SS). The notation for the standard uncertainty 𝑠S(RS;𝑚) includes the relevant sampling parameter, m. 𝑠S(SS) (2) 𝑠S(RS;𝑚) = 𝑚 Linear composite sampling uncertainty A linear composite sampling (LS) involves collecting m subsamples, starting from the centre of the sampling circle, and obtaining the other (m-1) subsamples in a radial line at d meters intervals. The subsamples collected inside the sampling circle are mixed in the same container producing the composite sample. This sampling type can be more accurately described than the random sampling that can become inadequate by collecting subsamples from close positions. The determination of LS standard uncertainty, 𝑠S(LS), is equivalent to the determination of 𝑠S(SS) but instead of determining zh from points randomly drawn from the sampling circle, groups of zh are determined from points of a line. For each radial line to the sampling center, the mean, 𝑧ℎ(𝑚;𝑑), of m zh estimates the value of a composite linear sample. The standard deviation of 𝑧ℎ(𝑚;𝑑), 𝑠z(𝑚;𝑑), can be used to estimate the standard uncertainty from linear composite sampling, 𝑠S(LS) (eq 3). 𝑠2r 2 (3) 𝑠S(LS;𝑚;𝑑) = 𝑠z (𝑚;𝑑) ― 𝑚 The repeatability of the mean (𝑠r 𝑚) is subtracted to 𝑠z(𝑚;𝑑) since 𝑧ℎ(𝑚;𝑑) is the mean of m simulated zh affected by the measurement repeatability. The 𝑠S(LS;𝑚;𝑑) should be smaller than 𝑠S(SS). River water parameter uncertainty The standard uncertainty, 𝑢(𝑞SC), of the estimated river water parameter, 𝑞SC, in the sampling circle is calculated by combining the pertaining sampling uncertainty with sample analysis uncertainty. The analyzed sample can be a single sample or a composite sample. Eq 4 describes the calculation of 𝑢(𝑞SC) where 𝑠S can be 𝑠S(SS), 𝑠S(RS) or 𝑠S(LS) depending of the sampling type. ACS Paragon Plus Environment


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(4) 𝑢(𝑞SC) = 𝑠2S +𝑠2I + 𝑢2T where 𝑠I and 𝑢T are the standard deviation of measurement intermediate precision (also known as between-days precision) and the standard uncertainty of measurement trueness, respectively. The 𝑢T quantifies the impact of systematic effects on the analysis of the water sample and is estimated from the performance observed in the analysis of reference water samples (i.e. samples with a known value of the analyzed parameter)19,20. Eq 4 can be used directly to estimate 𝑢(𝑞SC) by using 𝑠S, 𝑠I and 𝑢T calculated for the level of the parameter 𝑞SC. All these uncertainty components have the units of 𝑞SC. Eq 3 is also applicable to the calculation of 𝑢(𝑞SC) in Interval I: [𝑞LOD; 2 𝑞LOQ [. However, for Internal II, a relative standard uncertainty, 𝑢′(𝑞SC), is estimated by using an equation equivalent to eq 4 where relative standard deviations or standard uncertainty are considered (eq 5). (5) 𝑢′(𝑞SC) = 𝑠′2S +𝑠′2I + 𝑢′T2 where 𝑠′S, 𝑠′I and 𝑢′T are the relative standard deviation of sampling and intermediate precision, and trueness standard uncertainty, respectively. The 𝑢(𝑞SC) and 𝑢′(𝑞SC) can be expanded to approximately 95 % or 99 % confidence level to obtain the expanded, 𝑈(𝑞), and relative expanded, 𝑈′(𝑞), uncertainties by using a coverage factor, k, of 2 or 3, respectively (e.g. 𝑈(𝑞) = 𝑘𝑢(𝑞)). In this work, the 𝑠′I and 𝑢′T were estimated by the top-down approach for the evaluation of the measurement uncertainty described by Cordeiro et al.19. Sampling uncertainty extrapolation The calculated sampling uncertainty, function of sampling type, can be used directly to calculate the uncertainty of a quantity determined in the same river area in another occasion. The applicability of the sampling uncertainty model can be checked by comparing the results of duplicate single samplings. If the range of results, A, is not larger than a repeatability limit that includes the sampling (i.e., 𝐴 ≤ 2.8𝑠(𝑆𝑆)), it can be concluded that the heterogeneity of the system did not vary significantly. In that case, the calculated 𝑠(𝑆𝑆), 𝑠(𝑅𝑆) and 𝑠(𝐿𝑆) can be used in that occasion. This extrapolation assumes that quantity values are quantified in the same quantity interval: I or II. For another river system with equivalent heterogeneity (e.g. a second location close to the one studied in detail), similar extrapolation can be attempted if it is also checked from results of duplicate single samplings. The detailed assessment of the spatial distribution of the quantity level in the new sampling circle can protect assessments from wrong extrapolations of the sampling uncertainty. Target uncertainty for river systems comparison The models of sampling and combined uncertainty variation with the type and number of collected subsamples can be used to decide which sampling strategy should be used. The selection of the sampling strategy should be based on the minimum difference of the parameter to be distinguished, 𝐷Min, in the studied river systems. A river system is defined as the water at a specific river area, depth, date and time. The studied river systems can be the same river area on different occasions or different river areas of the same or different rivers. The target (i.e. maximum admissible) standard uncertainty, 𝑢tg(𝑞SC), for 𝑞SC should be 4.2 times smaller than 𝐷Min: 𝑢tg (𝑞SC) = 𝐷Min 4.2. For instance, to distinguish a relative difference of 10 % of a parameter in two river systems, for a confidence level of 99 %, that parameter must be quantified with a relative standard uncertainty not larger than 2.4 %15,16. If a target expanded uncertainty, associated with a coverage factor or 2, is required, 𝑈tg(𝑞SC): 𝑈tg(𝑞SC) = 𝐷Min 2.1. EXPERIMENTAL In order to assess the spatial variation of nutrients (NOx, NO2, PO4 and SiO2) concentrations in the water of a Tagus river area at a specific depth, date and time, ten samples of 4 L to 5 L were collected, at 1 m depth, inside the sampling circle. The geographical coordinates of the sampling points were recorded and samples were coded sequentially as S1 to S10. The sampling circle has a larger wideness of approximately 350 m. The size of the sampling circle is the larger one that can be sampled from a boat in equivalent tide conditions. The sampling was performed on 20 January 2017, between 14:45 and 15:15, from a 27 m long ship using an 8 L Niskin sampler. The determination of sampling positions was performed by using a Garmin GPSmap 62s - GPS tracking equipment with a maximum coordinates error of 3 m. The distance between sampling points S9 and S10 is smaller than ten times the coordinates’ error, but this did not affect the modelling. Figure 2 represents the sampling positions in the river map and Table S1 of the Supporting Information the respective geographic coordinates. Upon collection, the samples were kept away from the light and heat until delivered at the laboratory after less than 5 hours, were independently homogenized and filtered using a 0.45 μm pore size cartridge (Pall, AquaPrep 600), and a 100 mL volume of filtered water retained in high-density polyethylene bottles for analysis. The samples were preserved at temperatures below -20 ºC until analysis, performed less than one month after sampling. ACS Paragon Plus Environment

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The determination of nutrients concentrations in the samples (nitrate+nitrite – NOx, nitrite – NO2, reactive phosphorus – PO4 and reactive silica – SiO2) was performed by UV/Vis spectroscopy using specific colorimetric methods implemented in a Skalar SANplus Segmented Flow AutoAnalyzer specially engineered for the analysis of saline waters. NOx and NO2 were determined according to Strickland and Parsons21, PO4 was determined according to Murphy and Riley22 and SiO2 was determined according to Koroleff23. All procedures were adapted to segmented flow analysis. Measurements were performed by validated procedures and their quality controlled through the analysis of blank samples, control standards close to the LOQ and in the middle of the calibration interval, duplicate samples and spiked samples. Metrologically sound criteria were used to accept these controls19,20. The ‘Division of Chemistry and Marine Pollution’ of the Portuguese Navy’s ‘Hydrographic Institute’ (IHPT), that performed the analyses, is accredited by the Portuguese Accreditation Body, IPAC, following the ISO/IEC 17025:2005 standard24 for the determination of these parameters in saline (estuarine and marine) water. The most relevant performance parameters of sample measurements are presented in the Supporting Information. The sampling data was processed by the user-friendly MS-Excel file “Sampling_Uncertainty.xlsm” available as Supporting Information. This file only requires that the user enters the coordinates of the “ground” and sampling points, the performance of the procedure used for sample analysis, and the measured values of the n samples. The spreadsheet calculates the sampling uncertainty from the selected sampling type: SS or LS. The spreadsheet allows describing the spatial distribution of the parameter in the sampling circle from up to 20 sampling points. The assessment of the sampling can be based on 20000 or 40000 simulation lines. More information about the spreadsheet is provided in the text file of the Supporting Information. RESULTS AND DISCUSSION Table S2 presents the performance of nutrients determination in water samples required to calculate the combined standard uncertainty (eq 4 or eq 5). Figure 1 (nitrite results) and Table S3 present the measured nutrients concentrations in the analyzed samples (S1 to S10) where the reported expanded uncertainties do not include the sampling component. Figure 1 also presents the 3D surface that describes the spatial variation of nitrite concentration in the sampling circle that was subject to the described randomization to estimate the sampling uncertainty. For all studied parameters, the simulated 𝑧ℎ that scanned the sampling circle has a symmetric distribution that was assumed to be approximately normal for simplicity. Even if some deviations to normality are observed, the concentration of composite samples tend to be normal as the number of mixed subsamples, m, increases. Single sampling (SS) The line “SS” of Table 1 presents the mean, 𝑧, and the relative standard deviation, 𝑠′,(i.e. 𝑠′(SS)) of simulated z values of nitrite concentrations that scanned the sampling circle. This table also presents the other performance parameters required to calculate the uncertainty of river water parameter, where 𝑠′2S = 𝑠′2 ― 𝑠′2r. The performance of single samplings of the other nutrients is described in the Supporting Information (Table S4). Relative standard uncertainties were reported since all determinations were performed above two times the Limit of Quantification (i.e. in Interval II of the analytical scope). The last column of Table 1 and Table S4 presents the relative expanded uncertainty of nutrient concentration in the sampling circle. The expanded uncertainties are associated with approximately 95 % confidence level and were calculated by using a coverage factor of 2. Figure 3 presents the simulated spatial variation of nitrite concentration in the sampling circle and Figure 4 the absolute frequency of simulated nitrite concentrations (Dashed line). Since concentration distribution is unimodal and rather symmetric, and only ten samples were collected inside the sampling circle, these data were treated assuming the normal distribution of values. The limited number of collected samples and the unpredictable impact of nutrients sources on river water suggest that the normal distribution of concentration values would be the more conservative model to study single samplings. Random (RS) and linear (LS) composite sampling Table 1 and Table S4 present the performance of Random (RS) or Linear (LS) composite samplings where the number of subsamples, m, and, for LS, also the distance between samplings, d, are defined. It were studied m from 2 to 7 and equidistant linear samplings in a range of 60 m to make sure all radial directions away from the sampling centre are inside the sampling circle. For RS, the 𝑠S that represents the intrinsic variability of nutrient concentration in composite samples, 𝑠S(RS;𝑚), obtained from m subsamples randomly drawn from the sampling circle, is estimated by eq 2. The 𝑠S(LS;𝑚;𝑑) was estimated numerically by simulating this sampling type (eq 3). The d varies between 60 m, 30 m, 20 m, 15 m, 12 m and 10 m for m equal to 2, 3, 4, 5, 6 and 7, respectively. Figure 4 presents the distribution of simulated nitrite concentrations in composite samples obtained by mixing seven subsamples collected in a line at 10 m intervals. The dispersion of estimates is significantly smaller than observed from single samplings. ACS Paragon Plus Environment


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Figure 5 and Figure S1 present 𝑠′S variation with sampling type and the respective 𝑈′ that quantifies the quality of concentration estimate in the sampling circle. Comparison of sampling strategies Tables 1 and S4, and Figures 5 and S1 allow concluding that a composite sampling is less uncertain than single a sampling, and that composite sampling uncertainty reduces as m increases, as expected. The reduction of 𝑠′S with the increase of m is less relevant for a larger number of subsamples. For the analysis of NO2 and PO4, LS is less uncertain than RS for the same m. However, for the determination of NOx, the RS is less uncertain than LS. For the determination of SiO2, it is not possible to distinguish the measurement repeatability from the simulated variability of composite samples concentration from LS; measurement repeatability is equivalent to 𝑠(LS). The uncertainty of RS is quantifiable since it is estimated from single sampling uncertainty (eq 2). The relative expanded uncertainty of measured nutrients concentrations in Tagus river water varies between 5.9 % to 10 %, being fit for detecting trends of nutrient levels larger than 12 % to 21 %, respectively (i.e. trends 2.1 times larger than the expanded uncertainty for k equal to 2)15,16. No relevant differences were observed between the mean values of simulated nutrients concentrations obtained from the studied samplings types, suggesting that LS is not affected by systematic effects. The LS is the sampling type that scans a smaller fraction of the sampling circle and, therefore, can be affected by systematic deviations. The mean of randomly selected 50 simulated values was compared with a t-test for a 99 % confidence level. For LS, it was not observed a continuous reduction of 𝑠′S as the number of subsamples increases due to the variability of the numerical determinations. The sampling is a major uncertainty component for the determinations of NOx and NO2, responsible for 21 % to 62 % of the global uncertainty. For PO4 measurements, the sampling uncertainty can be relevant for single samplings (24 % of the global uncertainty) or become negligible for composite samplings. The sampling uncertainty is negligible for the determination of SiO2. The relevance of the sampling uncertainty component depends on the relevance of parameter’s spatial heterogeneity given sample analysis uncertainty. For instance, in heterogeneous distributions of nutrients measured with low sample analysis uncertainty, the sampling uncertainty will be a relevant component of mean concentration estimate in the sample circle. CONCLUSIONS The developed methodology for evaluating and optimizing the sampling uncertainty was successfully applied to the determination of nutrients concentrations in Tagus river estuary. This evaluation is based on the numerical simulation of the spatial variation of analyte concentration in a river area based on results of samples collected in that area and on coordinates and sample analysis uncertainty. The modelled spatial variation of the parameter in the river allowed estimating the uncertainty from a Single Sampling (SS) or composite sampling by mixing m subsamples collected randomly (Random Sampling, RS) or in a line (Linear Sampling, LS) that crosses the river area. SS is more uncertain than a composite sampling that gets less uncertain as the number of subsamples increases. The improvement of the sampling with subsamples number increase is less pronounced in larger subsamples number. No relevant systematic difference was observed between concentration estimates obtained by the different sampling types: SS, RS and LS. The sampling uncertainty was combined with sample analysis uncertainty to estimate parameter concentration in the river area with uncertainty. For the studied nutrients and river water area, the sampling relative standard uncertainty ranged from 0.31 % to 4.4 % producing relative expanded uncertainties of nutrients concentrations, for approximately 95 % confidence level, between 5.9 % and 10 % (coverage factor of 2). This uncertainty allows detecting differences in nutrients concentrations at different occasions of the same river area between 12 % and 21 % for a confidence level of 99 %. The sampling uncertainties were evaluated by using a user-friendly and validated MS-Excel file available as Supporting Information. ASSOCIATE CONTENT The Supporting Information is available free of charge on the ACS Publications website at DOI: (…). The MS-Excel file used for sampling uncertainty evaluation, and additional data and details about sampling quality are provided. ACKNOWLEDGEMENTS This work was supported by Fundacão para a Ciência e Tecnologia (FCT) under project UID/QUI/00100/2013 and scholarship SFRH/BPD/110186/2015. The authors also thank Instituto Hidrográfico for the use of the official nautical charts 21101 and 26307 in Figure 2.

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REFERENCES (1) Water quality - Sampling - Part 9: Guidance on sampling from marine waters - ISO 5667-9:1992; ISO, Geneva, 1992. (2) Water quality - Sampling - Part 1: Guidance on the design of sampling programmes and sampling techniques - ISO 5667-1:2006; ISO, Geneva, 2006. (3) Analytical Measurements in Aquatic Environments, Namiesnik, J., Szefer, P. Eds.; CRC Press, 2017. (4) Harmel, R.D., King, K.W., Considerations in selecting a water quality sampling strategy, Transactions of the ASAE, 2003, 46(1), 63–73. (5) Halliday, S. J., Wade, A. J., Skeffington, R. A., Neal, C., Reynolds, B., Rowland, P., Neal, M., Norris, D., An analysis of long-term trends, seasonality and short-term dynamics in water quality data from Plynlimon, Wales, Science of the Total Environment, 2012, 434, 186–200. (6) Behmel, S., Damour, M., Ludwig, R., Rodriguez, M. J., Water quality monitoring strategies — A review and future perspectives, Science of the Total Environment, 2016, 571, 1312–1329. (7) Luhtala, H., Tolvanen, H., Spatio-temporal representativeness of euphotic depth in situ sampling in transitional coastal waters, Journal of Sea Research, 2016, 112, 32–40. (8) Ramsey, M. H., Sampling as a source of measurement uncertainty: techniques for quantification and comparison with analytical sources, J. Anal. At. Spectrom. 1998, 13, 97–104. (9) Eurachem/ EUROLAB/ CITAC/ Nordtest/ AMC guide: Measurement uncertainty arising from sampling: a guide to methods and approaches, Ramsey, M. H., Ellison, S. L. R. Eds; Eurachem, 2007. (10) Madrid, Y., Zayas. Z.P., Water sampling: Traditional methods and new approaches in water sampling strategy, Trend. Anal. Chem., 2007, 26(4), 293-299. (11) Lardy-Fontan, S., Brieudes, V., Lalere, B., Candido, P., Couturier, G., Budzinski, H., Lavison-Bompard, G., For more reliable measurements of pharmaceuticals in the environment: Overall measurement uncertainty estimation, QA/QC implementation and metrological considerations. A case study on the Seine River, Trends in Analytical Chemistry, 2016, 77, 76–86. (12) International Vocabulary of Metrology – Basic and General Concepts and Associated Terms (VIM 3rd edition) JCGM 200, JCGM; BIPM, 2012. (13) Evaluation of measurement data – Guide to the expression of uncertainty in measurement (GUM) JCGM 100, JCGM; BIPM, 2012. (14) Eurachem/CITAC guide: Quantifying uncertainty in analytical measurement, 3rd ed., Ellison, S. L. R., Williams, A. Eds.; Eurachem, 2012. (15) Silva R. J. N. B., Setting Target Measurement Uncertainty in Water Analysis, Water 2013, 5, 1279–1302. (16) Eurachem/CITAC Guide: Setting and Using Target Uncertainty in Chemical Measurement, Silva, R. J. B., Williams, A. Eds.; Eurachem, 2015. (17) Accuracy (trueness and precision) of measurement methods and results - Part 6: Use in practice of accuracy values - ISO 5725-6:1994; Genève, ISO, 1994. (18) Statistics for the Quality Control Laboratory, Mullins, E.; Royal Society of Chemistry, Cambridge, 2003. (19) Cordeiro, R. M. S., Rosa, C. M. G., Silva, R. J. N. B., Measurements recovery evaluation from the analysis of independent reference materials: Analysis of different samples with native quantity spiked at different levels, Accred Qual Assur 2018, 23, 57–71. (20) Palma, C., Morgado, V., Silva, R. J. N. B., Top-down evaluation of matrix effects uncertainty, Talanta 2018, 192, 278–287. (21) Strickland, J. D. H., Parsons, T. R., A Practical Handbook of Seawater Analysis. Fisheries Research Board of Canada, Ottawa, 1972. (22) Murphy, J., Riley, J. P., A modified single solution method for the determination of phosphate in natural waters, Anal. Chim. Acta 1962, 27, 31–36. (23) Koroleff, F., Determination of ammonia. In: Grasshoff, K. (Ed.), Methods of Seawater Analysis. Verlag Chemie, New York, 1976, pp. 126–158. (24) ISO/IEC 17025:2005, General requirements for the competence of testing and calibration laboratories; ISO, Geneva, 2005.



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Table 1. Simulated variability of estimated nitrite concentration in a Tagus river estuary area, and associated relative sampling and expanded uncertainties from different sampling types. 𝑠′r (%) 𝑠′S (%) § 𝑠′I (%) 𝑢′T (%) 𝑠′ (%) § 𝑈′ (%) Sampling Mean § SS 0.444 4.45 0.87 4.36 2.11 1.31 10.2 RS(2) 3.21 0.87 3.09 2.11 1.31 8.11 RS(3) 2.67 0.87 2.52 2.11 1.31 7.29 RS(4) 2.35 0.87 2.18 2.11 1.31 6.84 RS(5) 2.14 0.87 1.95 2.11 1.31 6.56 RS(6) 1.98 0.87 1.78 2.11 1.31 6.36 RS(7) 1.87 0.87 1.65 2.11 1.31 6.21 LS(2; 60) 0.436 1.93 0.87 1.83 2.11 1.31 6.41 LS(3; 30) 0.436 1.70 0.87 1.62 2.11 1.31 6.18 LS(4; 20) 0.435 1.40 0.87 1.33 2.11 1.31 5.90 LS(5; 15) 0.436 1.42 0.87 1.36 2.11 1.31 5.93 LS(6; 12) 0.436 1.28 0.87 1.23 2.11 1.31 5.81 LS(7; 10) 0.436 1.41 0.87 1.37 2.11 1.31 5.94 § - Value obtained by the Monte Carlo Method; SS - Single sampling; RS(m) - Random composite sampling from m subsamples; LS(m; d) - Linear composite sampling from m subsamples positioned at d meters.

Figure 1. Variation of nitrite concentration in the studied Tagus river area at 1 m depth estimated from ten sampling points (S1 to S10). The coordinates of the sampling points (x, y) were defined by taking a geographic origin. The z axis represents the concentration values, c(NO2). This information was used to build a 3D surface represented by a combination of various triangular surfaces. The circle presented in one of the triangular surfaces (S2;S3;S4) represents the estimated nitrite concentration, zh, in the geographic coordinate (xh, yh).


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Figure 2. The position of the sampling points (S1 to S10) in Tagus river estuary map (implanted over a partial reproduction of the official nautical charts 21101 and 26307, edited by Instituto Hidrográfico - these reproductions are not fit for navigation purposes). The geographic origin is identified as “Ground”.

Figure 3. Simulated variability of nitrite concentration in 1 m depth water of the studied Tagus river area.



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Figure 4. Distribution of simulated nitrite concentrations in 1 m depth water samples of a Tagus river area obtained from ‘Single Samplings’ (SS) or “Linear Composite Samplings” (LS;7;10) of seven subsamples collected in a line at 10 m intervals.

Figure 5. Variation of sampling relative standard uncertainty, 𝑠′S, and of nitrite concentration relative expanded uncertainty, 𝑈′, in the studied Tagus river area with the sampling type. The studied samplings types are ‘Single sampling’ (SS), ‘Random composite sampling’ (RS) and ‘Linear composite sampling’ (LS) based on mixing m subsamples. The LS covered a range of 60 m, where the distance between subsamples is 60 m, 30 m, 20 m, 15 m,12 m or 10 m for a subsamples number, m, equal to 2, 3, 4, 5, 6 or 7, respectively.


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For TOC only:



Figure 1. Variation of nitrite concentration in the studied Tagus river area at 1 m depth estimated from ten sampling points (S1 to S10). The coordinates of the sampling points (x, y) were defined by taking a geographic origin. The z axis represents the concentration values, c(NO2). This information was used to build a 3D surface represented by a combination of various triangular surfaces. The circle presented in one of the triangular surfaces (S2;S3;S4) represents the estimated nitrite concentration, zh, in the geographic coordinate (xh, yh).


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Figure 2. The position of the sampling points (S1 to S10) in Tagus river estuary map (implanted over a partial reproduction of the official nautical charts 21101 and 26307, edited by Instituto Hidrográfico - these reproductions are not fit for navigation purposes). The geographic origin is identified as “Ground”.



Figure 3. Simulated variability of nitrite concentration in 1 m depth water of the studied Tagus river area.


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Figure 4. Distribution of simulated nitrite concentrations in 1 m depth water samples of a Tagus river area obtained from ‘Single Samplings’ (SS) or “Linear Composite Samplings” (LS;7;10) of seven subsamples collected in a line at 10 m intervals.



Figure 5. Variation of sampling relative standard uncertainty, s'S, and of nitrite concentration relative expanded uncertainty, U', in the studied Tagus river area with the sampling type. The studied samplings types are ‘Single sampling’ (SS), ‘Random composite sampling’ (RS) and ‘Linear composite sampling’ (LS) based on mixing m subsamples. The LS covered a range of 60 m, where the distance between subsamples is 60 m, 30 m, 20 m, 15 m,12 m or 10 m for a subsamples number, m, equal to 2, 3, 4, 5, 6 or 7, respectively.


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Figure S1. Variation of sampling relative standard uncertainty, s'S, and of nutrient concentration relative expanded uncertainty, U', in the studied Tagus river area with sampling type. The studied sampling types are ‘Single sampling’ (SS), ‘Random composite sampling’ (RS) and ‘Linear composite sampling’ (LS) based on mixing m subsamples. The LS covered a range of 60 m, where the distance between subsamples is 60 m, 30 m, 20 m, 15 m,12 m or 10 m for a number of subsamples, m, equal to 2, 3, 4, 5, 6 or 7, respectively.


Optimization of River Sampling: Application to Nutrients Distribution in

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