Measurement uncertainty analysis provides a quantitative statement of the reliability of sulfur dioxide (SO2) determination results and is a mandatory technical requirement for laboratories accredited to ISO/IEC 17025. This article presents a systematic framework for identifying, quantifying, and reporting the uncertainty components associated with SO2 testing in ambient air, stationary source emissions, and food matrices, following the methodology of ISO/IEC Guide 98-3 (GUM). Readers will learn how to construct an uncertainty budget, calculate combined and expanded uncertainty, and correctly express final test results.
Technical Overview
Measurement uncertainty is a parameter associated with the result of a measurement that characterizes the dispersion of the values that could reasonably be attributed to the measurand. For sulfur dioxide determination, a complete test report does not merely state a single concentration value; it must also convey how much confidence can be placed in that value. Uncertainty analysis is therefore an essential element of quality control, method validation, and conformity assessment in accredited third-party laboratories.
The internationally recognized framework for this work is the Guide to the Expression of Uncertainty in Measurement (GUM), published as ISO/IEC Guide 98-3 and supplemented by ISO/IEC Guide 98-3 Supplement 1 for numerical propagation methods such as Monte Carlo simulation. In China, the corresponding implementation documents are JJF 1059.1 and GB/T 27418. Clause 7.6 of ISO/IEC 17025 requires testing laboratories to identify the contributions to measurement uncertainty and to report expanded uncertainty when it is relevant to the validity or application of the results, when a customer requests it, or when a statement of conformity is issued against a specification limit.
Uncertainty components are evaluated by two complementary approaches. Type A evaluation uses statistical analysis of repeated observations, typically the standard deviation of replicate determinations. Type B evaluation relies on other sources of information, such as calibration certificates, reference material certificates, manufacturer specifications, glassware tolerance limits, and published method data. All components, regardless of their origin, are expressed as standard uncertainties and combined using the law of propagation of uncertainty.
Testing Samples
Ambient and Indoor Air
Ambient air samples are collected into absorption solutions using impingers or diffusive samplers, or measured in situ by automated analyzers. Typical reported concentrations range from a few micrograms per cubic meter in clean background locations to several milligrams per cubic meter near industrial sources.
Stationary Source Emissions
Flue gas samples from boilers, kilns, incinerators, and industrial furnaces are extracted with heated probes using isokinetic or constant-flow sampling in accordance with GB/T 16157. SO2 concentrations in these matrices are commonly in the range of tens to thousands of milligrams per cubic meter, and regulatory compliance decisions depend directly on the measurement result.
Food and Agricultural Products
Sulfur dioxide and sulfite residues are determined in dried fruits, preserved vegetables, wine, beer, starch, sugar, and traditional Chinese herbal medicines. In these matrices, the result is expressed as total SO2, usually in milligrams per kilogram, following the sample preparation and distillation procedures of GB 5009.34.
Water and Wastewater
Free and bound sulfite in surface water, groundwater, and treated effluent is determined by spectrophotometry, iodometric titration, or ion chromatography, with results reported as SO2 or sulfite equivalents.
Workplace Atmospheres
Occupational exposure assessments require the determination of SO2 in breathing-zone air collected with personal sampling pumps, evaluated against occupational exposure limits.
Testing Items
The primary testing item is the mass concentration of sulfur dioxide in the sampled matrix, expressed in milligrams per cubic meter for air and emission samples or in grams per kilogram or milligrams per kilogram for food matrices. In food testing, the measurand is the total sulfur dioxide content, which includes both free sulfite and reversibly bound sulfite released during acidic distillation. Supporting items within the uncertainty evaluation include the standard-state sampling volume, the absorbance response of the analytical instrument, the concentration of calibration standards, and the recovery efficiency of the complete analytical procedure.
Testing Methods
Formaldehyde Absorption-Pararosaniline Spectrophotometry
SO2 is absorbed in formaldehyde buffer solution to form hydroxymethanesulfonate, which reacts with pararosaniline and formaldehyde to produce a purple-red dye measured at 577 nm. This principle underlies HJ 482 and HJ 483 for ambient air and remains one of the most widely validated manual methods, although the use of mercuric salts in older variants has been restricted for environmental reasons.
UV Fluorescence
SO2 molecules excited by ultraviolet radiation fluoresce at longer wavelengths, and the fluorescence intensity is proportional to concentration. EN 14212 specifies this principle for ambient air monitoring, and it is the dominant technology in continuous air quality analyzers.
Non-Dispersive Infrared Absorption
SO2 absorbs infrared radiation in characteristic bands. HJ 629 specifies the non-dispersive infrared method for stationary source emissions, offering high selectivity and automated operation.
Fixed Potential Electrolysis
HJ 57 specifies electrochemical sensor cells for portable and on-site SO2 measurement in flue gas. The sensor current is proportional to the SO2 concentration, and calibration against certified gas standards is a major uncertainty driver.
Distillation-Titration and Spectrophotometric Methods for Food
GB 5009.34 specifies the determination of total SO2 in foods by acidic distillation followed by iodometric titration, oxidation-acid-base titration, or spectrophotometric detection of the distilled SO2 after absorption. Distillation recovery and titration endpoint judgment are the dominant uncertainty contributors.
Ion Chromatography
After collection or oxidation, sulfate and sulfite species can be separated and quantified by ion chromatography with conductivity detection, providing excellent sensitivity and multi-species capability.
Mathematical Model of the Measurement
A clear functional relationship between the measurand and all input quantities is the starting point of any uncertainty evaluation. For the spectrophotometric determination of SO2 in air, a typical model is expressed as follows.
C(SO2) = (A − a) / b × Vt / Vs, where A is the measured absorbance of the sample solution, a and b are the intercept and slope of the calibration curve, Vt is the total volume of absorption solution, and Vs is the sampling volume converted to standard conditions.
The standard-state sampling volume is itself calculated from measured quantities: Vs = Q × t × (Pa / 101.325) × (273.15 / (273.15 + T)), where Q is the average flow rate, t is the sampling duration, Pa is the atmospheric pressure, and T is the sample gas temperature. Each of these input quantities carries its own uncertainty component.
For food samples analyzed by distillation and titration, the model takes the form W(SO2) = c × (V − V0) × M / m × f, where c is the titrant molarity, V and V0 are the titration volumes of sample and blank, M is the molar mass conversion factor, m is the test portion mass, and f is the recovery correction factor.
Uncertainty Source Analysis
Sampling Volume Components
Contributions arise from the calibration uncertainty of the flow meter or sampling pump, the accuracy of the flow indicator, the timing device, and the correction of gas volume to standard temperature and pressure. For isokinetic sampling in ducts, the measurement of nozzle diameter, stack pressure, and stack temperature introduces additional terms.
Standard Solution Preparation
The certified purity or concentration of the SO2 standard material taken from the certificate of a certified reference material is a Type B component. Serial dilution from stock to working standards adds uncertainty from the calibration tolerances of pipettes and volumetric flasks and from temperature effects on volume. Rectangularly distributed tolerance limits are converted to standard uncertainties by division by the square root of three.
Calibration Curve Fitting
Regression of absorbance against concentration produces residual scatter that propagates into every interpolated sample result. The standard uncertainty of the interpolated concentration C0 is calculated as u(C0) = (S / b) × sqrt(1/p + 1/n + (C0 − Cbar)² / Sxx), where S is the residual standard deviation of the regression, n is the number of calibration points, p is the number of replicate measurements of the sample, and Sxx is the sum of squared deviations of the calibration concentrations from their mean. Minimizing this component requires an adequate number of calibration points spanning the sample concentration and careful reagent preparation.
Instrument Reading
The resolution of the spectrophotometer display, photometric drift, and wavelength accuracy contribute small but quantifiable terms. For automated analyzers, the signal noise and zero and span drift specifications from calibration certificates are used.
Method Repeatability
The standard deviation of replicate determinations of the same sample, normalized as a relative standard deviation, is the Type A component. It integrates the random variation of sampling, reagent handling, and instrument response.
Recovery and Matrix Effects
In food analysis, incomplete release of bound sulfite during distillation, loss of SO2 during transfer, and matrix interferences in the titration cause systematic bias. If recovery is not corrected, its variability must be included as an uncertainty component based on validation data or spiked sample studies.
Environmental and Reagent Blank Effects
Laboratory temperature fluctuations, reagent purity, and blank absorbance variation contribute additional, usually minor, components that should nonetheless be listed in the budget for completeness.
Evaluation and Calculation Procedure
The evaluation proceeds through six defined steps: specification of the measurand and the functional model; identification of all uncertainty sources; quantification of each component as a standard uncertainty; determination of sensitivity coefficients, which equal one for purely multiplicative models; combination of the components; and expansion to the chosen level of confidence.
For multiplicative models, it is convenient to work with relative standard uncertainties. The combined relative uncertainty is calculated as ucrel = sqrt(u1² + u2² + ... + un²), where each term is a relative standard uncertainty contribution. The expanded uncertainty is then U = k × uc, with the coverage factor k = 2 providing a coverage probability of approximately 95% under the assumption of a normal distribution.
A representative illustrative budget for a spectrophotometric ambient air determination at a level of 0.521 milligrams per cubic meter is listed below.
- Sampling volume, including flow, timer, temperature and pressure corrections: 1.6 percent
- Certified reference material for the SO2 stock solution: 0.5 percent
- Serial dilution using volumetric glassware: 0.8 percent
- Calibration curve regression and interpolation: 1.8 percent
- Absorbance measurement and spectrophotometer resolution: 0.6 percent
- Sample solution volume and transfer operations: 0.7 percent
- Repeatability of replicate determinations: 1.5 percent
- Combined relative standard uncertainty: 3.1 percent
- Expanded relative uncertainty at k = 2: 6.3 percent
The result would therefore be reported as 0.521 milligrams per cubic meter plus or minus 0.033 milligrams per cubic meter, with a coverage factor of k = 2 corresponding to a coverage probability of approximately 95 percent. For food matrices analyzed by distillation-titration, expanded relative uncertainties of 5 to 10 percent are commonly achieved, driven mainly by recovery variability and titration volume measurement.
Reporting of Results
In accordance with ISO/IEC 17025, when uncertainty is reported, the test report must state the expanded uncertainty together with the coverage factor and the associated coverage probability. The symbol U is used for expanded uncertainty, and the unit must match the unit of the measurand. When statements of conformity are issued, the laboratory must apply a documented decision rule that takes measurement uncertainty into account, for example by applying simple acceptance, guard-banded acceptance, or shared-risk approaches as agreed with the client.
The uncertainty budget should be maintained as a controlled technical record and reviewed whenever the method, instruments, reagents, or critical personnel change, or at defined periodic intervals, because a previously valid budget may no longer represent current laboratory conditions.
Applications
- Demonstrating technical competence during ISO/IEC 17025 accreditation assessments and proficiency testing schemes.
- Supporting regulatory compliance decisions for SO2 emission limits in stationary sources and ambient air quality standards.
- Verifying food safety compliance against maximum residue limits for sulfur dioxide and sulfites in preserved and processed foods.
- Calibrating and auditing continuous emission monitoring systems against standardized reference methods.
- Comparing laboratory results across sites and time periods by placing measured differences in the context of their uncertainty intervals.
- Optimizing methods by identifying the dominant uncertainty contributors and prioritizing improvement actions such as better glassware, additional calibration points, or automated titration.
FAQ
What is the difference between measurement error and measurement uncertainty?
Error is a single signed difference between a measured value and a true value, which is never known exactly. Uncertainty is a non-negative parameter characterizing a range of values within which the true value is believed to lie with a stated probability. Error is a conceptual notion, while uncertainty is a quantifiable property of the measurement result.
Why is a coverage factor of k = 2 commonly used?
For a result whose effective degrees of freedom are large and whose distribution is approximately normal, multiplying the combined standard uncertainty by 2 yields an interval with a coverage probability of approximately 95 percent, which is the conventional confidence level for reporting test results.
What are Type A and Type B evaluations?
Type A evaluation calculates uncertainty from the statistical distribution of repeated observations, such as the standard deviation of replicate sample determinations. Type B evaluation derives uncertainty from other knowledge, including calibration certificates, reference material certificates, glassware tolerances, instrument specifications, and published data, with assumed distributions such as rectangular or triangular.
What level of expanded uncertainty is acceptable for SO2 determination?
There is no universal limit, because acceptability depends on the method, matrix, and concentration level. Well-controlled spectrophotometric and instrumental air methods typically achieve expanded relative uncertainties between 4 and 10 percent, while food distillation-titration methods commonly fall between 5 and 12 percent. The key requirement is that the reported interval must remain fit for the intended compliance decision.
How can the uncertainty of SO2 results be reduced?
Effective measures include using calibrated glassware and certified reference materials, increasing the number of calibration points and replicate measurements, selecting calibration standards that bracket the sample concentration, controlling laboratory temperature, improving distillation recovery, and replacing manual titration with automated potentiometric endpoint detection.
Is uncertainty evaluation mandatory for every routine SO2 test?
The uncertainty budget is established and validated during method validation and then reviewed periodically; it does not need to be recalculated for every routine sample. However, the expanded uncertainty must be reported when it is relevant to result validity, when a client requests it, or when a statement of conformity against a limit is issued.
Conclusion
A rigorous uncertainty analysis transforms a single-point SO2 determination into a defensible, metrologically traceable result. By systematically modeling the measurement, identifying each contributing component, and combining the components according to the GUM framework, accredited third-party laboratories can report expanded uncertainties that are technically justified, support sound conformity decisions, and satisfy the requirements of ISO/IEC 17025 and the associated national and international test method standards.