Evaluation and implementation of measurement uncertainty for determining stationary source emissions: a review

  • Jhon J. Cárdenas-Monsalve Instituto Tecnológico Metropolitano
  • Andrés F. Ramírez-Barrera Instituto Tecnológico Metropolitano
  • Edilson Delgado-Trejos Instituto Tecnológico Metropolitano
Keywords: Measurement uncertainty, Guide to the Expression of Uncertainty in Measurement GUM, Monte Carlo method, stochastic methods


This paper presents a review of commonly-cited methods for estimating uncertainty in the literature. One of them is the non-stochastic approach proposed by the Guide to the Expression of Uncertainty in Measurement (GUM), which provides an estimation framework with limitations for the implementation, such as computation of partial derivatives, linear model assumptions, and uncertainty source identification with probability distributions. Other methods to estimate uncertainty are discussed as well; they include Monte Carlo, Fuzzy Sets, Generalized Intervals, Bayesian Inference, Polynomial Chaos, and Bootstrap, which in contrast to GUM present limitations regarding computational cost and require more specialized knowledge to be implemented. The aim of this work is to report the level of application and dissemination of methods for estimating the uncertainty of emissions caused by stationary sources. Most of the works in this field were found to be focused on the creation of inventories of Greenhouse Gases (GHG), and very few of them on the uncertainty associated with measuring the emissions of stationary sources using direct reading monitoring or those defined by the Environmental Protection Agency of the United States (US EPA). Finally, strengths and weaknesses are discussed in order to promote new research in this knowledge area.


Download data is not yet available.

Author Biographies

Jhon J. Cárdenas-Monsalve, Instituto Tecnológico Metropolitano

Ingeniero Químico, Especialista en Salud Ocupacional

Andrés F. Ramírez-Barrera, Instituto Tecnológico Metropolitano

Bioingeniero, Magíster en Administración, Departamento Académico, Facultad de Ingenierías

Edilson Delgado-Trejos, Instituto Tecnológico Metropolitano

PhD Ingeniería LI Automática, MSc Automatización Industrial, Ingeniero Electrónico, Departamento de Calidad y Producción, Facultad de Ciencias Económicas y Administrativas


[1] J. M. Booker and T. J. Ross, “An evolution of uncertainty assessment and quantification,” Sci. Iran., vol. 18, no. 3, pp. 669–676, Jun. 2011.
[2] BIPM et al., International vocabulary of metrology-Basic and general concepts and associated terms (VIM), 3rd ed. JCGM, 2012.
[3] D. Romano, A. Bernetti, and R. De Lauretis, “Different methodologies to quantify uncertainties of air emissions,” Environ. Int., vol. 30, no. 8, pp. 1099–1107, Oct. 2004.
[4] H.-J. von Martens, “Evaluation of uncertainty in measurements—problems and tools,” Opt. Lasers Eng., vol. 38, no. 3–4, pp. 185–206, Sep. 2002.
[5] BIPM et al., Evaluation of measurement data - Guide to the expression of uncertainty in measurement. JCGM, 2008.
[6] BIPM et al., Evaluation of measurement data - An introduction to the “Guide to the expression of uncertainty in measurement” and related documents. JCGM, 2009.
[7] BIPM et al., Evaluation of measurement data - Supplement 2 to the “Guide to the expression of uncertainty in measurement” - Extension to any number of output quantities. JCGM, 2011.
[8] K. Rypdal and K. Flugsrud, “Sensitivity analysis as a tool for systematic reductions in greenhouse gas inventory uncertainties,” Environ. Sci. Policy, vol. 4, no. 2–3, pp. 117–135, Apr. 2001.
[9] O. Velychko and T. Gordiyenko, “The use of guide to the expression of uncertainty in measurement for uncertainty management in National Greenhouse Gas Inventories,” Int. J. Greenh. Gas Control, vol. 3, no. 4, pp. 514–517, Jul. 2009.
[10] O. N. Velichko and T. B. Gordienko, “Methods of calculating emissions of pollutants into the atmosphere and estimating their uncertainty,” Meas. Tech., vol. 52, no. 2, pp. 193–199, Feb. 2009.
[11] L.-I. Tong, C.-W. Chang, S.-E. Jin, and R. Saminathan, “Quantifying uncertainty of emission estimates in National Greenhouse Gas Inventories using bootstrap confidence intervals,” Atmos. Environ., vol. 56, pp. 80–87, Sep. 2012.
[12] A. Ferrero and S. Salicone, “The random-fuzzy variables: A new approach to the expression of uncertainty in measurement,” IEEE Trans. Instrum. Meas., vol. 53, no. 5, pp. 1370–1377, 2004.
[13] H. Cheng and A. Sandu, “Uncertainty quantification and apportionment in air quality models using the polynomial chaos method,” Environ. Model. Softw., vol. 24, no. 8, pp. 917–925, Aug. 2009.
[14] J. I. DelaRosa and G. A. Fleury, “Bootstrap Methods for a Measurement Estimation Problem,” IEEE Trans. Instrum. Meas., vol. 55, no. 3, pp. 820–827, Jun. 2006.
[15] I. Lira and D. Grientschnig, “Equivalence of alternative Bayesian procedures for evaluating measurement uncertainty,” Metrologia, vol. 47, no. 3, pp. 334–336, 2010.
[16] Y. Hu, F. Xie, B. Wu, and Y. Wang, “An Uncertainty Quantification Method Based on Generalized Interval,” in 2013 12th Mexican International Conference on Artificial Intelligence, 2013, pp. 145–150.
[17] G. Buonanno, G. Ficco, C. Liguori, and A. Pietrosanto, “The influence of the uncertainty on monitoring stack emissions in a waste-to-energy plant,” in 2008 IEEE Instrumentation and Measurement Technology Conference, 2008, pp. 1771–1776.
[18] Legal Information Institute, “Environmental Protection Agency,” in CFR, Legal Information Institute.
[19] Instituto de Hidrología, Meteorología y Estudios Ambientales de Colombia - IDEAM, Resolución 935. Colombia, 2011.
[20] J. F. P. Gomes, V. M. a Cruz, and M. L. C. Ribeiro, “Estimation of uncertainty in the determination of nitrogen oxides emissions,” Accredit. Qual. Assur., vol. 11, no. 3, pp. 138–145, May 2006.
[21] BIPM et al., Evaluation of measurement data - Supplement 1 to the “Guide to the expression of uncertainty in measurement” - Propagation of distributions using a Monte Carlo method. JCGM, 2008.
[22] M. A. Azpurua, C. Tremola, and E. Paez Barrios, “Comparison of the Gum and Monte Carlo Methods for the Uncertainty Estimation in Electromagnetic Compatibility Testing,” Prog. Electromagn. Res. B, vol. 34, pp. 125–144, 2011.
[23] H. Ramebäck et al., “Implementing combined uncertainty according to GUM into a commercial gamma spectrometric software,” J. Radioanal. Nucl. Chem., vol. 282, no. 3, pp. 979–983, Dec. 2009.
[24] EURACHEM and CITAC, Quantifying Uncertainty in Analytical Measurements, 3rd ed. Germany, 2012.
[25] M. A. L. Traple, A. M. Saviano, F. L. Francisco, and F. R. Lourenço, “Measurement uncertainty in pharmaceutical analysis and its application,” J. Pharm. Anal., vol. 4, no. 1, pp. 1–5, Feb. 2014.
[26] J. Choi, E. Hwang, H. Y. So, and B. Kim, “An uncertainty evaluation for multiple measurements by GUM,” Accredit. Qual. Assur., vol. 8, no. 1, pp. 13–15, 2003.
[27] J. Choi, D. Kim, E. Hwang, and H.-Y. So, “An uncertainty evaluation for multiple measurements by GUM, II,” Accredit. Qual. Assur., vol. 8, no. 5, pp. 205–2017, 2003.
[28] S. G. Rabinovich, “Accuracy of single measurements,” Accredit. Qual. Assur., vol. 12, no. 8, pp. 419–424, Aug. 2007.
[29] R. Kessel, M. Berglund, and R. Wellum, “Application of consistency checking to evaluation of uncertainty in multiple replicate measurements,” Accredit. Qual. Assur., vol. 13, no. 6, pp. 293–298, Jun. 2008.
[30] M. Priel, “From GUM to alternative methods for measurement uncertainty evaluation,” Accredit. Qual. Assur., vol. 14, no. 5, pp. 235–241, 2009.
[31] G. Nam, C.-S. Kang, H.-Y. So, and J. Choi, “An uncertainty evaluation for multiple measurements by GUM, III: using a correlation coefficient,” Accredit. Qual. Assur., vol. 14, no. 1, pp. 43–47, Jan. 2009.
[32] F. Attivissimo, A. Cataldo, L. Fabbiano, and N. Giaquinto, “Systematic errors and measurement uncertainty: An experimental approach,” Measurement, vol. 44, no. 9, pp. 1781–1789, Nov. 2011.
[33] M. A. F. Martins, R. Requião, and R. A. Kalid, “Generalized expressions of second and third order for the evaluation of standard measurement uncertainty,” Measurement, vol. 44, no. 9, pp. 1526–1530, Nov. 2011.
[34] A. Williams, “EURACHEM/CITAC workshop on recent developments in measurement uncertainty,” Accredit. Qual. Assur., vol. 17, no. 2, pp. 111–113, Apr. 2012.
[35] P. Wei, Q. P. Yang, M. R. Salleh, and B. Jones, “Symbolic Computation for Evaluation of Measurement Uncertainty,” in 2007 IEEE Instrumentation & Measurement Technology Conference IMTC 2007, 2007, pp. 1–4.
[36] J. M. Jurado and A. Alcázar, “A software package comparison for uncertainty measurement estimation according to GUM,” Accredit. Qual. Assur., vol. 10, no. 7, pp. 373–381, Jul. 2005.
[37] T. a. Zang, “On the expression of uncertainty intervals in engineering,” Theor. Comput. Fluid Dyn., vol. 26, no. 5, pp. 403–414, Oct. 2012.
[38] F. Attivissimo, N. Giaquinto, and M. Savino, “A Bayesian paradox and its impact on the GUM approach to uncertainty,” Measurement, vol. 45, no. 9, pp. 2194–2202, Nov. 2012.
[39] H. Imai, “Expanding needs for metrological traceability and measurement uncertainty,” Measurement, vol. 46, no. 8, pp. 2942–2945, Oct. 2013.
[40] M. Thompson and S. L. R. Ellison, “Dark uncertainty,” Accredit. Qual. Assur., vol. 16, no. 10, pp. 483–487, Oct. 2011.
[41] G. Chew and T. Walczyk, “A Monte Carlo approach for estimating measurement uncertainty using standard spreadsheet software,” Anal. Bioanal. Chem., vol. 402, no. 7, pp. 2463–2469, Mar. 2012.
[42] M. Cox, P. Harris, and B. R.-L. Siebert, “Evaluation of Measurement Uncertainty Based on the Propagation of Distributions Using Monte Carlo Simulation,” Meas. Tech., vol. 46, no. 9, pp. 824–833, Sep. 2003.
[43] M. Ángeles Herrador and A. G. González, “Evaluation of measurement uncertainty in analytical assays by means of Monte-Carlo simulation,” Talanta, vol. 64, no. 2, pp. 415–422, Oct. 2004.
[44] M. G. Cox and B. R. L. Siebert, “The use of a Monte Carlo method for evaluating uncertainty and expanded uncertainty,” Metrologia, vol. 43, no. 4, pp. S178–S188, Aug. 2006.
[45] A. B. Forbes, “An MCMC algorithm based on GUM Supplement 1 for uncertainty evaluation,” Measurement, vol. 45, no. 5, pp. 1188–1199, Jun. 2012.
[46] H. Janssen, “Monte-Carlo based uncertainty analysis: Sampling efficiency and sampling convergence,” Reliab. Eng. Syst. Saf., vol. 109, pp. 123–132, Jan. 2013.
[47] D. a. Sheen and H. Wang, “The method of uncertainty quantification and minimization using polynomial chaos expansions,” Combust. Flame, vol. 158, no. 12, pp. 2358–2374, Dec. 2011.
[48] E. D. Attanasi and T. C. Coburn, “A Bootstrap Approach to Computing Uncertainty in Inferred Oil and Gas Reserve Estimates,” Nat. Resour. Res., vol. 13, no. 1, pp. 45–52, Mar. 2004.
[49] T. Saffaj and B. Ihssane, “A Bayesian approach for application to method validation and measurement uncertainty,” Talanta, vol. 92, pp. 15–25, Apr. 2012.
[50] I. Park and R. V Grandhi, “A Bayesian statistical method for quantifying model form uncertainty and two model combination methods,” Reliab. Eng. Syst. Saf., vol. 129, pp. 46–56, Sep. 2014.
[51] D. Theodorou, L. Meligotsidou, S. Karavoltsos, A. Burnetas, M. Dassenakis, and M. Scoullos, “Comparison of ISO-GUM and Monte Carlo methods for the evaluation of measurement uncertainty: Application to direct cadmium measurement in water by GFAAS,” Talanta, vol. 83, no. 5, pp. 1568–1574, Feb. 2011.
[52] D. Theodorou, Y. Zannikou, G. Anastopoulos, and F. Zannikos, “Coverage interval estimation of the measurement of Gross Heat of Combustion of fuel by bomb calorimetry: Comparison of ISO GUM and adaptive Monte Carlo method,” Thermochim. Acta, vol. 526, no. 1–2, pp. 122–129, Nov. 2011.
[53] S. Sediva and M. Havlikova, “Comparison of GUM and Monte Carlo method for evaluation measurement uncertainty of indirect measurements,” in Proceedings of the 14th International Carpathian Control Conference (ICCC), 2013, pp. 325–329.
[54] A. E. Torres-Abello, “Metodología para la Estimación de Incertidumbres Asociadas a Concentraciones de Sólidos Suspendidos Totales Mediante Métodos de Generación Aleatoria,” TecnoLógicas, no. 26, pp. 181–200, 2011.
[55] M. G. Cox, “Propagation of distributions by a Monte Carlo method, with an application to ratio models,” Eur. Phys. J. Spec. Top., vol. 172, no. 1, pp. 153–162, Jun. 2009.
[56] T. E. Lovett, F. Ponci, and A. Monti, “A Polynomial Chaos Approach to Measurement Uncertainty,” IEEE Trans. Instrum. Meas., vol. 55, no. 3, pp. 729–736, Jun. 2006.
[57] R. Bun, K. Hamal, M. Gusti, and A. Bun, “Spatial GHG inventory at the regional level: accounting for uncertainty,” Clim. Change, vol. 103, no. 1–2, pp. 227–244, Nov. 2010.
[58] M. Lesiv, A. Bun, and M. Jonas, “Analysis of change in relative uncertainty in GHG emissions from stationary sources for the EU 15,” Clim. Change, vol. 124, no. 3, pp. 505–518, Jun. 2014.
[59] K. Rypdal and W. Winiwarter, “Uncertainties in greenhouse gas emission inventories — evaluation, comparability and implications,” Environ. Sci. Policy, vol. 4, no. 2–3, pp. 107–116, Apr. 2001.
[60] H. C. Frey and J. Zheng, “Quantification of Variability and Uncertainty in Emission Inventories: A Prototype Software Tool with Application to Utility NOx Emissions,” Proceedings, Annu. Meet. Air Waste Manag. Assoc., p. 19, Sep. 2001.
How to Cite
Cárdenas-Monsalve, J., Ramírez-Barrera, A., & Delgado-Trejos, E. (2018, May 14). Evaluation and implementation of measurement uncertainty for determining stationary source emissions: a review. TecnoLógicas, 21(42), 231-244. https://doi.org/10.22430/22565337.790
Review Article

Most read articles by the same author(s)