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Climate Change: Use of Non-Homogeneous Poisson Processes for Climate Data in Presence of a Change-Point

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Abstract

In this study, non-homogeneous Poisson processes (NHPP) are used to analyze climate data. The data were collected over a certain period time and consist of the yearly average precipitation, yearly average temperature and yearly average maximum temperature for some regions of the world. Different existing parametric forms depending on time and on unknown parameters are assumed for the intensity/rate function \(\lambda (t), t \ge 0\) of the NHPP. In the present context, the Poisson events of interest are the numbers of years that a climate variable measurement has exceeded a given threshold of interest. The threshold corresponds to the overall average measurements of each climate variable taking into account here. Two versions of the NHPP model are considered in the study, one version without including change points and one version including a change point. The parameters included in the model are estimated under a Bayesian approach using standard Markov chain Monte Carlo (MCMC) methods such as the Gibbs sampling and Metropolis–Hastings algorithms. The models are applied to climate data from Kazakhstan and Uzbekistan, in Central Asia and from the USA obtained over several years.

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Data Availability

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Acknowledgements

The authors are grateful to an anonymous reviewer for the comments and suggestions which helped to improve the presentation of the results and also for suggesting the work about Hawkes processes. The authors are also grateful to Dr Eliane R. Rodrigues for a review of the manuscript and important comments that led to the great improvement of the article.

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Authors and Affiliations

  1. Medical School, University of São Paulo, São Paulo, Brazil

    Jorge Alberto Achcar

  2. Department of the Environment, Maringá State University, Maringá, Brazil

    Ricardo Puziol de Oliveira

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  1. Jorge Alberto Achcar
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Jorge Alberto Achcar and Ricardo Puziol de Oliveira contributed to revision, writing, analysis and methodology.

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Correspondence to Ricardo Puziol de Oliveira.

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Appendices

Appendix 1

Table 5 A1. Average yearly precipitation in Kazakhstan (Almaty) from the year 1879 to 2002
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Table 6 A2. Average yearly maximum temperature in Kazakhstan (Almaty) from the year 1915 to 2003
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Table 7 A3. Average yearly maximum temperature in Uzbekistan (Tashkent) from the year 1894 to 2003
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Table 8 A4. Average yearly temperature in USA from the year 1895 to 2019
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Appendix 2

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Achcar, J.A., de Oliveira, R.P. Climate Change: Use of Non-Homogeneous Poisson Processes for Climate Data in Presence of a Change-Point. Environ Model Assess 27, 385–398 (2022). https://doi.org/10.1007/s10666-021-09797-z

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