DETECTION OF POINTS OF CLIMATIC CHANGES, A BAYESIAN APPROACH IN CLIMATIC DATA OF THE CITY OF SÃO PAULO
Points of climatic changes, a Bayesian approach
Abstract
In this study, we introduce a statistical model applied to climate change data (annual mean temperature and annual mean rain precipitation for a long period) obtained from a climate station in São Paulo City Brazil. The assumed model used in the data analysis consists of an autoregressive times series (AR) model which represents a type of random process. A Bayesian approach using MCMC (Markov Chain Monte Carlo) methods is considered to get the inferences of interest. The main goal of the study is to have a fitted statistical model to get good predictions for annual mean temperature and annual mean rain precipitation and also to be used to identify the time of possible climate change-points.
References
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Arnell N W, Lloyd-Hughes B (2014) The global-scale impacts of climate change on water resources and flooding under new climate and socio-economic scenarios. Climatic Change 122:127-140. doi:10.1007/s10584-013-0948-4.
Bacon D W, Watts, D G (1971), Estimating the Transition between Two Intersecting Straight Lines. Biometrika, 58(3):525 - 534.
Barnard GA (1959) Control charts and stochastic processes. Journal of the Royal Statistical Society, B,21(2): 239-271.
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Carlin B P, Gelfand A E, Smith A F (1992) Hierarchical Bayesian analysis of change point problems. Journal of the Royal Statistical Society Series C Applied statistics 41(2):389{405. https://doi.org/10.2307/2347570
Chib S. , Greenberg E. (1995). Understanding the Metropolis-Hastings algorithm, The American Statistician, 49(4), 327-335.
Costello A, Abbas M, Allen A, Ball S et al. (2009) Managing the health effects of climate change. The Lancet 373:1693-1733.
Diaz-Nieto J, Wilby R L (2005) A comparison of statistical downscaling and climate change factor methods: impacts on low ows in the River Thames, United Kingdom. Climatic Change 69(2):245-268. doi:10.1007/s10584-005-1157-6
Grigg OA, Farewell VT, Spiegelhalter DJ et al. (2003). The use of risk-adjusted CUSUM and RSPRT charts for monitoring in medical contexts. Statistical Methods in Medical Research. 12 (2): 147–170.
Ferreira P E (1975), A Bayesian Analysis of a Switching Regression Model: Known Number of Regimes, Journal of the American Statistical Association 70(350):370-374.
Gallagher C, Lund R, Robbins M (2012) Changepoint detection in daily precipitation data. Environmetrics, 23:407- 419. doi: 10.1002/env.2146
Gelfand A E, Smith A F (1990). Sampling-based approaches to calculating marginal densities. Journal of the American Statistical Association 85(410):398 - 409.
Gelman A, Carlin J B, Stern H S, Rubin D B (1995) Bayesian data analysis. Chapman and Hall/CRC, New York.
Gilks W R, Richardson S, Spiegelhalter D (1995) Markov Chain Monte Carlo in practice. CRC Press, New York.
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Levermann A, Clark P U, Marzeion B, Milne G A et al. (2013) The multimillennial sea-level commitment of global warming. Proceedings of the National Academy of Sciences 110(34):13745-13750. doi:10.1073/pnas.1219414110
Li S, Lund R (2012). Multiple change-point detection via genetic algorithms. Journal of Climate 25(2):674 - 686. doi: 10.1175/2011JCLI4055.1
Lineman M, Do Y, Kim J Y, Joo G J (2015) Talking about climate change and global warming, PLOS ONE 10:e0138996. doi:10.1371/journal.pone.0138996.
Lunn D. J., Thomas A., Best N., Spiegelhalter D. (2000). OpenBugs: a Bayesian modelling framework: concepts, structure, and extensibility. Statistics and Computing, 10(4), 325-337.
Matthews T. (2018) Humid heat and climate change. Progress in Physical Geography: Earth and Environment 42(3):391- 405. doi:10.1177/0309133318776490.
Montgomery D.C., Jennings C.L., Kulahci M. (2008). Introduction to Time Series Analysis and Forecasting. John Wiley & Sons, Inc.
NOAA (2021) National Centers for Environmental Information. State of the climate:global climate report for 2020. https://www.ncdc.noaa.gov/sotc/global/202013.
NRC (2011) National Research Council. Causes and consequences of climate change. America's climate choices. The National Academies Press. Washington, D.C.. doi:10.17226/12781. ISBN 978-0-309-14585-5.
Poloczanska E S, Brown C J, Sydeman W J, Kiessling W, et al. (2013) Global imprint of climate change on marine life. Nature Climate Change 3:919 - 925. doi:10.1038/nclimate1958.
Powell B (2016) Statistical modelling of climate change. In: Letcher T M (ed) Climate Change, 2nd Edition. Elsevier, New York, pp. 341 - 354. doi: /10.1016/B978-0-444- 63524-2.00022.
Ribes A, Zwiers F W, Azaiis J M. et al. (2017) A new statistical approach to climate change detection and attribution. Climate Dynamics 48(1-2):367- 386. doi:10.1007/s00382-016-30796
Richards G R (1993) Change in global temperature: a statistical analysis. Journal of Climate 6(3):546{659. https://doi.org/10.1175/1520.
Robbins M W, Gallagher C M, Lund R B (2016). A general regression changepoint test for time series data. Journal of the American Statistical Association 111(514): 670 - 683. doi:10.1080/01621459.2015.1029130
Serdeczny O, Adams S, Baarsch F, Coumou D. et al. (2016) Climate change impacts in Sub-Saharan Africa: from physical changes to their social repercussions. Regional Environmental Change 17(6):1585 -1600. doi:10.1007/s10113-015-0910-2.
Spiegelhalter D, Thomas A, Best N, Lunn D. (2007) OpenBugs user manual Version 3.0. 2. MRC Biostatistics Unit, Cambridge.
Spiegelhalter D, Best N G., Carlin B. P., Van Der Linde A. (2002) Bayesian measures of model complexity and fit, Journal of the Royal Statistical Society, Series B 64(4):583-639.
Springmann M, Mason-D'Croz D, Robinson S, Garnett T et al. (2016) Global and regional health e_ects of future food production under climate change: a modelling study. Lancet 387(10031):1937-1946. doi:10.1016/S0140-6736(15)01156-3.
Tebaldi C, Sanso_ B (2009) Joint projections of temperature and precipitation change from multiple climate models: a hierarchical Bayesian approach. Journal of the Royal Statistical Society: Series A Statistics in Society 172(1):83-106. doi:10.1111/J.1467- 985X.2008.00545.X
Turner M G, Calder W J,Cumming G S, Hughes T P et al. (2020) Climate change, ecosystems and abrupt change: science priorities. Philosophical Transactions of the Royal Society B. 375(1794):20190105. http://dx.doi.org/10.1098/rstb.2019.0105
Vanem E (2016) Joint statistical models for signi_cant wave height and wave period in a changing climate. Marine Structures 49(C): 180 - 205. doi:10.1016/j.marstruc.2016.06.001
Zhao C, Liu B et al. (2017) Temperature increase reduces global yields of major crops in four independent estimates. Proceedings of the National Academy of Sciences 114(35): 9326-9331. doi:10.1073/pnas.1701762114.
Alexander L V, Zhang X, Peterson T, Caesar J, Gleason B, Tank A M G, Haylock M, Collins D, Trevin B, Rahimzadeh F, Tagipou A, Kumar R K, Revadekar J, Griffths G, Vincent L, Stephenson D, Burn J, Aguillar E, Taylor M, New M, Zhai P, Rusticucci M, Vasquez-Aguirre J L (2006) Global observed changes in daily climate extremes of temperature and precipitation. Journal of Geophysical Research 111:D05109. doi:10.1029/2005JD006290.
Arnell N W, Lloyd-Hughes B (2014) The global-scale impacts of climate change on water resources and flooding under new climate and socio-economic scenarios. Climatic Change 122:127-140. doi:10.1007/s10584-013-0948-4.
Bacon D W, Watts, D G (1971), Estimating the Transition between Two Intersecting Straight Lines. Biometrika, 58(3):525 - 534.
Barnard GA (1959) Control charts and stochastic processes. Journal of the Royal Statistical Society, B,21(2): 239-271.
Barry D, Hartigan J A (1993). A Bayesian analysis for change point problems. Journal of the American Statistical Association 88(421):309 - 319.
Bell W.R. (1984). An Introduction to Forecasting with Time Series Models. Insurance: Mathematics and Economics,3: 241-255.
Bernardo, J.M. and Smith, A.F.M. (1994) Bayesian Theory. John Wiley and Sons Inc., New York. http://dx.doi.org/10.1002/9780470316870
Box G.E.P., Jenkins G.M., Reinsel G.C. (1994). Time Series Analysis: Forecasting and Control. Third Edition. Prentice Hall.
Box G. E. P., Tiao G. C. (1973). Bayesian inference in statistical analysis, Addison-Wesley Publishing Co, Reading, Mass. London-Don Mills.
Carlin B P, Gelfand A E, Smith A F (1992) Hierarchical Bayesian analysis of change point problems. Journal of the Royal Statistical Society Series C Applied statistics 41(2):389{405. https://doi.org/10.2307/2347570
Chib S. , Greenberg E. (1995). Understanding the Metropolis-Hastings algorithm, The American Statistician, 49(4), 327-335.
Costello A, Abbas M, Allen A, Ball S et al. (2009) Managing the health effects of climate change. The Lancet 373:1693-1733.
Diaz-Nieto J, Wilby R L (2005) A comparison of statistical downscaling and climate change factor methods: impacts on low ows in the River Thames, United Kingdom. Climatic Change 69(2):245-268. doi:10.1007/s10584-005-1157-6
Grigg OA, Farewell VT, Spiegelhalter DJ et al. (2003). The use of risk-adjusted CUSUM and RSPRT charts for monitoring in medical contexts. Statistical Methods in Medical Research. 12 (2): 147–170.
Ferreira P E (1975), A Bayesian Analysis of a Switching Regression Model: Known Number of Regimes, Journal of the American Statistical Association 70(350):370-374.
Gallagher C, Lund R, Robbins M (2012) Changepoint detection in daily precipitation data. Environmetrics, 23:407- 419. doi: 10.1002/env.2146
Gelfand A E, Smith A F (1990). Sampling-based approaches to calculating marginal densities. Journal of the American Statistical Association 85(410):398 - 409.
Gelman A, Carlin J B, Stern H S, Rubin D B (1995) Bayesian data analysis. Chapman and Hall/CRC, New York.
Gilks W R, Richardson S, Spiegelhalter D (1995) Markov Chain Monte Carlo in practice. CRC Press, New York.
Hawkins E, Ortega P, Suckling E, Schurer A et al. (2017) Estimating Changes in Global Temperature since the Preindustrial Period. Bulletin of the American Meteorological Society 98(9):1841-1856. doi:10.1175/bams-d-16-0007.1.
IPCC (2007) Intergovernmental Panel on Climate Change. Summary for Policymakers, in Climate Change 2007: impacts, adaptation and vulnerability. Contribution of Working Group II to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change, p.17. Cambridge University Press, Cambridge, UK
IPCC (2013) Intergovernmental Panel on Climate Change. Summary for Policymakers. In: Stocker T F, Qin D, Plattner G-K, Tignor M, Allen S K, Boschung J, Nauels A, Xia Y, Bex V, Midgley P M (eds.) Climate Change 2013: the physical Science basis. Contribution of Working Group I to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change. Cambridge University Press, Cambridge, UK
Kabir R, Khan H T A, Ball E, Caldwell K (2016) Climate Change Impact: The Experience of the Coastal Areas of Bangladesh Affected by Cyclones Sidr and Aila, Journal of Environmental and Public Health 2016:9654753. doi:10.1155/2016/9654753.
Kaczan DJ, Orgill-Meyer J (2020) The impact of climate change on migration: a synthesis of recent empirical insights. Climatic Change 158(3):281- 300. doi:10.1007/s10584-019-02560-0. S2CID 207988694.
Levermann A, Clark P U, Marzeion B, Milne G A et al. (2013) The multimillennial sea-level commitment of global warming. Proceedings of the National Academy of Sciences 110(34):13745-13750. doi:10.1073/pnas.1219414110
Li S, Lund R (2012). Multiple change-point detection via genetic algorithms. Journal of Climate 25(2):674 - 686. doi: 10.1175/2011JCLI4055.1
Lineman M, Do Y, Kim J Y, Joo G J (2015) Talking about climate change and global warming, PLOS ONE 10:e0138996. doi:10.1371/journal.pone.0138996.
Lunn D. J., Thomas A., Best N., Spiegelhalter D. (2000). OpenBugs: a Bayesian modelling framework: concepts, structure, and extensibility. Statistics and Computing, 10(4), 325-337.
Matthews T. (2018) Humid heat and climate change. Progress in Physical Geography: Earth and Environment 42(3):391- 405. doi:10.1177/0309133318776490.
Montgomery D.C., Jennings C.L., Kulahci M. (2008). Introduction to Time Series Analysis and Forecasting. John Wiley & Sons, Inc.
NOAA (2021) National Centers for Environmental Information. State of the climate:global climate report for 2020. https://www.ncdc.noaa.gov/sotc/global/202013.
NRC (2011) National Research Council. Causes and consequences of climate change. America's climate choices. The National Academies Press. Washington, D.C.. doi:10.17226/12781. ISBN 978-0-309-14585-5.
Poloczanska E S, Brown C J, Sydeman W J, Kiessling W, et al. (2013) Global imprint of climate change on marine life. Nature Climate Change 3:919 - 925. doi:10.1038/nclimate1958.
Powell B (2016) Statistical modelling of climate change. In: Letcher T M (ed) Climate Change, 2nd Edition. Elsevier, New York, pp. 341 - 354. doi: /10.1016/B978-0-444- 63524-2.00022.
Ribes A, Zwiers F W, Azaiis J M. et al. (2017) A new statistical approach to climate change detection and attribution. Climate Dynamics 48(1-2):367- 386. doi:10.1007/s00382-016-30796
Richards G R (1993) Change in global temperature: a statistical analysis. Journal of Climate 6(3):546{659. https://doi.org/10.1175/1520.
Robbins M W, Gallagher C M, Lund R B (2016). A general regression changepoint test for time series data. Journal of the American Statistical Association 111(514): 670 - 683. doi:10.1080/01621459.2015.1029130
Serdeczny O, Adams S, Baarsch F, Coumou D. et al. (2016) Climate change impacts in Sub-Saharan Africa: from physical changes to their social repercussions. Regional Environmental Change 17(6):1585 -1600. doi:10.1007/s10113-015-0910-2.
Spiegelhalter D, Thomas A, Best N, Lunn D. (2007) OpenBugs user manual Version 3.0. 2. MRC Biostatistics Unit, Cambridge.
Spiegelhalter D, Best N G., Carlin B. P., Van Der Linde A. (2002) Bayesian measures of model complexity and fit, Journal of the Royal Statistical Society, Series B 64(4):583-639.
Springmann M, Mason-D'Croz D, Robinson S, Garnett T et al. (2016) Global and regional health e_ects of future food production under climate change: a modelling study. Lancet 387(10031):1937-1946. doi:10.1016/S0140-6736(15)01156-3.
Tebaldi C, Sanso_ B (2009) Joint projections of temperature and precipitation change from multiple climate models: a hierarchical Bayesian approach. Journal of the Royal Statistical Society: Series A Statistics in Society 172(1):83-106. doi:10.1111/J.1467- 985X.2008.00545.X
Turner M G, Calder W J,Cumming G S, Hughes T P et al. (2020) Climate change, ecosystems and abrupt change: science priorities. Philosophical Transactions of the Royal Society B. 375(1794):20190105. http://dx.doi.org/10.1098/rstb.2019.0105
Vanem E (2016) Joint statistical models for signi_cant wave height and wave period in a changing climate. Marine Structures 49(C): 180 - 205. doi:10.1016/j.marstruc.2016.06.001
Zhao C, Liu B et al. (2017) Temperature increase reduces global yields of major crops in four independent estimates. Proceedings of the National Academy of Sciences 114(35): 9326-9331. doi:10.1073/pnas.1701762114.
Published
05/06/2026
How to Cite
BARILI, Emerson; ACHCAR, Jorge Alberto.
DETECTION OF POINTS OF CLIMATIC CHANGES, A BAYESIAN APPROACH IN CLIMATIC DATA OF THE CITY OF SÃO PAULO.
Mercator, Fortaleza, v. 25, june 2026.
ISSN 1984-2201.
Available at: <http://www.mercator.ufc.br/mercator/article/view/3873>. Date accessed: 06 june 2026.
doi: https://doi.org/10.4215/rm2026.e25012.
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