Skip to main content

Designing a statistical procedure for monitoring global carbon dioxide emissions

Climatic Change volume 166, Article number: 32 (2021) Cite this article

Abstract

Following the Paris Agreement of 2015, most countries have agreed to reduce their carbon dioxide (CO2) emissions according to individually set Nationally Determined Contributions. However, national CO2 emissions are reported by individual countries and cannot be directly measured or verified by third parties. Inherent weaknesses in the reporting methodology may misrepresent, typically an under-reporting of, the total national emissions. This paper applies the theory of sequential testing to design a statistical monitoring procedure that can be used to detect systematic under-reportings of CO2 emissions. Using simulations, we investigate how the proposed sequential testing procedure can be expected to work in practice. We find that, if emissions are reported faithfully, the test is correctly sized, while, if emissions are under-reported, detection time can be sufficiently fast to help inform the 5 yearly global “stocktake” of the Paris Agreement. We recommend the monitoring procedure be applied going forward as part of a larger portfolio of methods designed to verify future global CO2 emissions.

This is a preview of subscription content, access via your institution.

Access options

Buy single article

Instant access to the full article PDF.

USD 39.95

Price includes VAT (USA)
Tax calculation will be finalised during checkout.

Fig. 1
Fig. 2
Fig. 3

Notes

  1. http://www.globalcarbonproject.org/

  2. In the 2020 version of the reports, GCB2020, a new sink term, \({S_{t}^{C}}\), was introduced into the budget equation, which is an estimate of the carbon sink from cement carbonation. The magnitude of this sink is small and here we simply include it in the fossil fuel emission estimates as suggested in Friedlingstein et al. (2020, p. 3277).

  3. We write “\(\overset {P}{\rightarrow }\)” for convergence in probability.

  4. Although, prima facie, α = 32% might seem like a high significance level to consider, a similar threshold is often used by the IPCC, where events happening with a probability lower than 33% are termed “unlikely” (Mastrandrea et al. 2010, Table 1, p. 3). Choosing such a high significance level will facilitate early detection of potential misreporting of CO2 emissions; naturally, it comes with the caveat of a correspondingly high probability of making a Type I error.

  5. https://sites.google.com/site/mbennedsen/research/monitoring.

References

  • Anderson TW, Darling DA (1952) Asymptotic theory of certain goodness of fit criteria based on stochastic processes. Ann Math Stat 23(2):193–212

    Article  Google Scholar 

  • Aue A, Hörmann S, Horváth L, Hušková L, Steinebach J (2012) Sequential testing for the stability of high-frequency portfolio betas. Econ Theory 28(4):804–837

    Article  Google Scholar 

  • Aue A, Horváth L (2012) Structural breaks in time series. J Time Ser Anal 34(1):1–16

    Article  Google Scholar 

  • Benford F (1938) The law of anomalous numbers. Proc Am Philos Soc 78(4):551–572

    Google Scholar 

  • Chu C-SJ, Stinchcombe M, White H (1996) Monitoring structural change. Econometrica 64(5):1045–1065

    Article  Google Scholar 

  • Cole MA, Maddison DJ, Zhang L (2020) Testing the emission reduction claims of CDM projects using the Benford’s Law. Clim Chang 160(3):407–426

    Article  Google Scholar 

  • Dette H, Gösmann J (2020) A likelihood ratio approach to sequential change point detection for a general class of parameters. J Am Stat Assoc 115 (531):1361–1377

    Article  Google Scholar 

  • Dickey DA, Fuller WA (1979) Distribution of the estimators for autoregressive time series with a unit root. J Am Stat Assoc 74(366a):427–431

    Article  Google Scholar 

  • Dlugokencky E, Tans P (2018) Trends in atmospheric carbon dioxide. National Oceanic & Atmospheric Administration, Earth System Research Laboratory (NOAA/ESRL). http://www.esrl.noaa.gov/gmd/ccgg/trends/global.html

  • Duflo E, Greenstone M, Pande R, Ryan N (2013) Truth-telling by third-party auditors and the response of the polluting firms: experimental evidence from India. Q J Econ 128:1499–1545

    Article  Google Scholar 

  • Durbin J, Watson GS (1971) Testing for serial correlation in least squares regression. Biometrika 58(1):1–19

    Google Scholar 

  • Friedlingstein P, Jones MW, O’Sullivan M, et al. (2019) Global Carbon Budget 2019. Earth Syst Sci Data 11(4):1783–1838

    Article  Google Scholar 

  • Friedlingstein P, O’Sullivan M, Jones MW et al (2020) Global Carbon Budget 2020. Earth Syst Sci Data 12(4):3269–3340

    Article  Google Scholar 

  • Gasser T, Crepin L, Quilcaille Y, Houghton RA, Ciais P, Obersteiner M (2020) Historical CO2 emissions from land use and land cover change and their uncertainty. Biogeosciences 17(15):4075–4101

    Article  Google Scholar 

  • Ghanem D, Zhang J (2014) ‘Effortless Perfection’: do Chinese cities manipulate air pollution data? J Environ Econ Manag 68(2):203–225

    Article  Google Scholar 

  • Gilfillan D, Marland G, Boden T, Andres T. (2019) Global, regional, and national fossil-fuel CO2 emissions. https://energy.appstate.edu/CDIAC

  • Gösmann J, Kley T, Dette H (2021) A new approach for open-end sequential change point monitoring. J Time Ser Anal 42(1):63–84

    Article  Google Scholar 

  • Guan D, Liu Z, Lindner S, Hubacek K (2012) The gigatonne gap in China’s carbon dioxide inventories. Nat Clim Chang 2:672–675

    Article  Google Scholar 

  • Hakkarainen J, Ialongo I, Tamminen J (2016) Direct space-based observations of anthropogenic CO2 emission areas from OCO-2. Geophys Res Lett 43 (21):11,400–11,406

    Article  Google Scholar 

  • Hamilton JD (1994) Time series analysis. Princeton University Press, Princeton

    Book  Google Scholar 

  • Hansis E, Davis SJ, Pongratz J (2015) Relevance of methodological choices for accounting of land use change carbon fluxes. Global Biogeochem Cycles 29:1230–1246

    Article  Google Scholar 

  • Hinkley DV (1971) Inference about the change-point from cumulative sum tests. Biometrika 58(3):509–523

    Article  Google Scholar 

  • Horváth L, Hušková M, Kokoszka P, Steinebach J (2004) Monitoring changes in linear models. J Stat Plan Infer 126(1):225–251

    Article  Google Scholar 

  • Houghton RA, Nassikas AA (2017) Global and regional fluxes of carbon from land use and land cover change 1850-2015. Global Biogeochem Cycles 31:456–472

    Article  Google Scholar 

  • IPCC (2018) Special Report on Global Warming of 1.5°C. Technical report, Intergovernmental Panel on Climate Change

  • Janardanan R, Maksyutov S, Oda T, Saito M, Kaiser JW, Ganshin A, Stohl A, Matsunaga T, Yoshida Y, Yokota T (2016) Comparing GOSAT observations of localized CO2 enhancements by large emitters with inventory-based estimates. Geophys Res Lett 43(7):3486–3493

    Article  Google Scholar 

  • Jarque CM, Bera AK (1987) A test for normality of observations and regression residuals. Int Stat Rev 2:163–172

    Article  Google Scholar 

  • Korsbakken JI, Peters GP, Andrew RM (2016) Uncertainties around reductions in China’s coal use and CO2 emissions. Nat Clim Chang 6:687–690

    Article  Google Scholar 

  • Kwiatkowski D, Phillips PC, Schmidt P, Shin Y (1992) Testing the null hypothesis of stationarity against the alternative of a unit root: how sure are we that economic time series have a unit root? J Econ 54(1):159–178

    Article  Google Scholar 

  • Lai TL (1995) Sequential changepoint detection in quality control and dynamical systems. J R Stat Soc Ser B 57(4):613–658

    Google Scholar 

  • Le Quéré C, Andrew RM, Friedlingstein P, et al. (2018a) Global Carbon Budget 2017. Earth Syst Sci Data 10(1):405–448

    Article  Google Scholar 

  • Le Quéré C, Andrew RM, Friedlingstein P, et al. (2018b) Global Carbon Budget 2018. Earth Syst Sci Data 10(4):2141–2194

    Article  Google Scholar 

  • Ljung GM, Box GEP (1978) On a measure of lack of fit in time series models. Biometrika 65(2):297–303

    Article  Google Scholar 

  • Luderer G, Vrontisi Z, Bertram C, Edelenbosch OY, Pietzcker RC, Rogelj J, De Boer HS, Drouet L, Emmerling J, Fricko O, Fujimori S, Havlǐk Luderer, Iyer G, Keramidas K, Kitous K, Pehl M, Krey V, Riahi V, Saveyn B, Tavoni M, Van Vuuren DP, Kriegler E (2018) Residual fossil CO2 emissions in 1.5–2°C pathways. Nat Clim Chang 8(7):626–633

    Article  Google Scholar 

  • Marland G, Rotty RM (1984) Carbon dioxide emissions from fossil fuels: a procedure for estimation and results for 1950–1982. Tellus B 36B(4):232–261

    Article  Google Scholar 

  • Massey FJ (1951) The Kolmogorov-Smirnov test for goodness of fit. J Am Stat Assoc 46(253):68–78

    Article  Google Scholar 

  • Mastrandrea MD, Field CB, Stocker TF, Edenhofer O, Ebi KL, Frame DJ, Held H, Kriegler E, Mach KJ, Matschoss PR, Plattner G-K, Yohe GW, Zwiers FW (2010) Guidance note for lead authors of the IPCC Fifth Assessment Report on consistent treatment of uncertainties. Technical report, IPCC Cross-Working Group Meeting on Consistent Treatment of Uncertainties

  • Meinshausen M, Jeffery L, Guetschow J, Robiou du Pont Y, Rogelj J, Schaeffer M, Höhne N, den Elzen M, Oberthör S, Meinshausen N (2015) National post-2020 greenhouse gas targets and diversity-aware leadership. Nat Clim Chang 5(12):1098–1106

    Article  Google Scholar 

  • Millar RJ, Fuglestvedt JS, Friedlingstein P, Rogelj J, Grubb MJ, Matthews HD, Skeie RB, Forster PM, Frame DJ, Allen MR (2017) Emission budgets and pathways consistent with limiting warming to 1.5°C. Nat Geosci 10:741–747

    Article  Google Scholar 

  • Nature (2018) Rules for a safe climate. Editorial

  • Page ES (1954) Continuous inspection schemes. Biometrika 41 (1):100–115

    Article  Google Scholar 

  • Peters GP, Le Quéré C, Andrew RM, Canadell JG, Friedlingstein P, Ilyina T, Jackson RB, Joos F, Korsbakken JI, McKinley GA, Sitch S, Tans P (2017) Towards real-time verification of CO2 emissions. Nat Clim Chang 7(12):848–850

    Article  Google Scholar 

  • Ramdas A, Wainwright YFMJ, Jordan MI (2017) Online control of the false discovery rate with decaying memory. In: Advances in neural information processing systems, pp 5655–5664

  • Ramdas A, Zrnic T, Wainwright MJ, Jordan MI (2018) SAFFRON: an adaptive algorithm for online control of the false discovery rate. In: Proceedings of the 35th International Conference on Machine Learning, pp 4286–4294

  • Reeves J, Chen J, Wang XL, Lund R, Lu QQ (2007) A review and comparison of changepoint detection techniques for climate data. J Appl Meteorol Climatol 46(6):900–915

    Article  Google Scholar 

  • Sanderson BM, O’Neill BC, Tebaldi C (2016) What would it take to achieve the Paris temperature targets? Geophys Res Lett 43(13):7133–7142

    Article  Google Scholar 

  • Schwandner FM, Gunson MR, Miller CE, Carn SA, Eldering A, Krings T, Verhulst KR, Schimel DS, Nguyen HM, Crisp D, O’Dell CW, Osterman GB, Iraci LT, Podolske JR (2017) Spaceborne detection of localized carbon dioxide sources. Science 358(6360)

  • Schwarz G (1978) Estimating the dimension of a model. Ann Stat 6(2):461–464

    Article  Google Scholar 

  • Tanaka K, O’Neill BC (2018) The Paris Agreement zero-emissions goal is not always consistent with the 1.5°C and 2°C temperature targets. Nat Clim Chang 8(4):319–324

    Article  Google Scholar 

  • Tokarska KB, Gillett NP (2018) Cumulative carbon emissions budgets consistent with 1.5°C global warming. Nat Clim Chang 8(4):296–299

    Article  Google Scholar 

  • Transparency International (2013) Global corruption report: climate change. Routledge, London

    Book  Google Scholar 

  • UN (2017) Energy statistics yearbook. https://unstats.un.org/unsd/energystats/pubs/yearbook/, Technical report, United Nations Statistics Division

  • UN (2020) Guidelines for the annual questionnaire on energy statistics. https://unstats.un.org/unsd/energystats/questionnaire/documents/Energy-Questionnaire-Guidelines.pdf. Technical report, United Nations Statistics Division

  • UNFCCC (2015) Adoption of the Paris agreement. https://unfccc.int/resource/docs/2015/cop21/eng/l09r01.pdf. Technical report, United Nations Framework Convention on Climate Change

  • UNFCCC (2018a) Modalities, procedures and guidelines for the transparency framework for action and support referred to in Article 13 of the Paris Agreement. Technical report, Ad Hoc Working Group on the Paris Agreement. https://unfccc.int/sites/default/files/resource/APA-SBSTA-SBI.2018.Informal.2.Add_.6_1.pdf

  • UNFCCC (2018b) Reporting and review under the Paris agreement. https://unfccc.int/process-and-meetings/transparency-and-reporting/reporting-and-review-under-the-paris-agreement. Technical report, United Nations Framework Convention on Climate Change

  • UNFCCC (2018c). https://di.unfccc.int/time_series

  • UNFCCC (2019) Inventory review reports. https://unfccc.int/process-and-meetings/transparency-and-reporting/reporting-and-review-under-the-convention/greenhouse-gas-inventories-annex-i-parties/inventory-review-reports-2019. Technical report, United Nations Framework Convention on Climate Change

  • Unkel S, Farrington CP, Garthwaite PH, Robertson C, Andrews N (2012) Statistical methods for the prospective detection of infectious disease outbreaks: a review. J R Stat Soc Ser A Stat Soc 175(1):49–82

    Article  Google Scholar 

  • Zhang D, Zhang Q, Qi S, Huang J, Karplus VJ, Zhang X (2019) Integrity of firms’ emissions reporting in China’s early carbon markets. Nat Clim Chang 9(2):164–169

    Article  Google Scholar 

Download references

Acknowledgements

The author would like to thank Eric Hillebrand, Siem Jan Koopman, three anonymous referees, and participants in the session on “Climate change mitigation, impacts, and adaptation” at the European Geoscience Union (EGU) General Assembly, Vienna, 2019, for many helpful comments and suggestions on the manuscript.

Funding

Financial support from the Independent Research Fund Denmark for the project “Econometric Modeling of Climate Change” is acknowledged.

Author information

Authors and Affiliations

  1. Department of Economics and Business Economics and CREATES, Aarhus University, Fuglesangs Allé 4, 8210, Aarhus V, Denmark

    Mikkel Bennedsen

Authors
  1. Mikkel Bennedsen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mikkel Bennedsen.

Additional information

Availability of data and material

The data used in this paper are freely available online; see https://doi.org/10.18160/GCP-2020for the GCB2020 version.

Code availability

The MATLAB code used to produce the results of the paper is freely available at https://sites.google.com/site/mbennedsen/research/monitoring.

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Electronic supplementary material

Below is the link to the electronic supplementary material.

(PDF 699 KB)

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Bennedsen, M. Designing a statistical procedure for monitoring global carbon dioxide emissions. Climatic Change 166, 32 (2021). https://doi.org/10.1007/s10584-021-03123-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10584-021-03123-y

Keywords

  • CO2 emissions
  • Paris Agreement
  • Global Carbon Budget
  • Sequential testing