Prediction of Air Temperature in East Java using Spatial Extreme Value with Copula Approach

A'yunin Sofro; Wildan Habibulloh; Khusnia Nurul Khikmah

doi:10.31764/jtam.v8i4.25436

Prediction of Air Temperature in East Java using Spatial Extreme Value with Copula Approach

A'yunin Sofro, Wildan Habibulloh, Khusnia Nurul Khikmah

Abstract

The increase in world temperature or global warming is a form of imbalance in the average temperature on Earth. The increase in air temperature will increase the risk of disasters, which will occur more frequently in the future. Rising global temperatures are expected to cause changes that can have fatal consequences. To anticipate the dangers are predicted by predicting the future air temperature increase. One of the methods that can be used is spatial extreme value theory, which uses the Gaussian copula model approach and Student's t copula, where the choice of these two methods was based on the flexibility they offer in capturing tail dependencies due to their capacity to describe the dependence structure between many variables simultaneously. . This makes it possible to get a return level or predicted value of air temperature by considering the elements of location in it. This research discusses both approaches and uses the maximum likelihood estimation (MLE) and pseudo maximum likelihood estimation (PMLE) methods to estimate the parameters. In addition, since spatial elements need to be considered, the trend surface model is also used. Akaike information criterion (AIC) is used to determine the best model for predicting air temperature based on extreme n air temperature data in East Java Province from nine air temperature observation stations. The results show that the highest air temperature value is around the Banyuwangi temperature observation station located in Banyuwangi Regency in the next two-year return period. The AIC results show that the best model produced is the Gaussian copula approach with a smaller AIC value than the student's t-copula approach, which is 8.0174. This value used to compare the relative quality of different statistical models with a lower AIC value generally indicates a better-fitting model.This value with a lower AIC value generally indicates a better-fitting model.

Keywords

Air temperature; Copula; Gaussian; Extreme values; Spatial;

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References

Ahmed, M., Ahmad, S., & Kheir, A. M. S. (2023). Climate change: an overview. Global Agricultural Production: Resilience to Climate Change, 1–30. https://doi.org/10.1007/978-3-031-14973-3_1.

Artha, A. A., & Sofro, A. (2019). Rainfall prediction in east java using spatial extreme value theory. Journal of Physics: Conference Series, 1417(1), 012010. https://doi.org/10.1088/1742-6596/1417/1/012010.

Boulaguiem, Y., Zscheischler, J., Vignotto, E., van der Wiel, K., & Engelke, S. (2022). Modeling and simulating spatial extremes by combining extreme value theory with generative adversarial networks. Environmental Data Science, 1, e5. https://doi.org/10.1017/eds.2022.4.

Carreau, J., & Toulemonde, G. (2020). Extra-parametrized extreme value copula: Extension to a spatial framework. Spatial Statistics, 40, https://doi.org/10.1016/j.spasta.2020.100410.

Cavanaugh, J. E., & Neath, A. A. (2019). The Akaike information criterion: Background, derivation, properties, application, interpretation, and refinements. Wiley Interdisciplinary Reviews: Computational Statistics, 11(3), https://doi.org/10.1002/wics.1460.

Cressie, N., & Moores, M. T. (2023). Spatial statistics. In Encyclopedia of mathematical geosciences (pp. 1362–1373). Springer. https://doi.org/10.1007/978-3-030-85040-1_31.

Czado, C., & Nagler, T. (2022). Vine copula based modeling. Annual Review of Statistics and Its Application, 9(1), 453–477. https://doi.org/10.1146/annurev-statistics-040220-101153.

Engelke, S., & Hitz, A. S. (2020). Graphical models for extremes. Journal of the Royal Statistical Society Series B: Statistical Methodology, 82(4), 871–932. https://doi.org/10.1111/rssb.12355.

Fauziyah, M., & Purnomo, J. D. T. (2020). Spatial extreme modeling using student t copula approach in Ngawi Regency. Journal of Physics: Conference Series, 1538(1), 012051. https://doi.org/10.1088/1742-6596/1538/1/012051.

Geenens, G. (2020). Copula modeling for discrete random vectors. Dependence Modeling, 8(1), 417–440. https://doi.org/10.1515/demo-2020-0022

Gimeno-Sotelo, L., & Gimeno, L. (2022). Concurrent extreme events of atmospheric moisture transport and precipitation: the role of atmospheric rivers. Authorea Preprints. https://doi.org/10.1002/essoar.10508750.3.

Guermah, T., & Rassoul, A. (2020). Study of extreme rainfalls using extreme value theory (case study: Khemis-Miliana region, Algeria). Communications in Statistics: Case Studies, Data Analysis and Applications, 6(3), 364–379. https://doi.org/10.1080/23737484.2020.1789901.

Hussain, F., Li, Y., Arun, A., & Haque, M. M. (2022). A hybrid modelling framework of machine learning and extreme value theory for crash risk estimation using traffic conflicts. Analytic Methods in Accident Research, 36, https://doi.org/10.1016/j.amar.2022.100248.

Hussain, S. I., & Li, S. (2022). Dependence structure between oil and other commodity futures in China based on extreme value theory and copulas. The World Economy, 45(1), 317–335. https://doi.org/10.1111/twec.13123.

Melina, Sukono, Napitupulu, H., & Mohamed, N. (2023). A conceptual model of investment-risk prediction in the stock market using extreme value theory with machine learning: a semisystematic literature review. Risks, 11(3), 60. https://doi.org/10.3390/risks11030060.

Min, J. L. J., & Halim, S. A. (2020). Rainfall modelling using generalized extreme value distribution with cyclic covariate. Mathematics and Statistics, 8(6), 762–772. https://doi.org/10.13189/ms.2020.080617.

Naveau, P., Hannart, A., & Ribes, A. (2020). Statistical methods for extreme event attribution in climate science. Annual Review of Statistics and Its Application, 7(1), 89–110. https://doi.org/10.1146/annurev-statistics-031219-041314.

Nazeri Tahroudi, M., Ramezani, Y., De Michele, C., & Mirabbasi, R. (2021). Flood routing via a copula-based approach. Hydrology Research, 52(6), 1294–1308. https://doi.org/10.2166/nh.2021.008.

Orsini, F., Gecchele, G., Gastaldi, M., & Rossi, R. (2020). Large‐scale road safety evaluation using extreme value theory. IET Intelligent Transport Systems, 14(9), 1004–1012. https://doi.org/10.1049/iet-its.2019.0633.

Portet, S. (2020). A primer on model selection using the Akaike Information Criterion. Infectious Disease Modelling, 5, 111–128. https://doi.org/10.1016/j.idm.2019.12.010.

Ramadhani, F. A., Nurrohmah, S., & Novita, M. (2017). Extreme value theory (EVT) application on estimating the distribution of maxima. AIP Conference Proceedings, 1862(1). https://doi.org/10.1063/1.4991260.

Rypkema, D., & Tuljapurkar, S. (2021). Modeling extreme climatic events using the generalized extreme value (GEV) distribution. In Handbook of Statistics (Vol. 44, pp. 39–71). Elsevier. https://doi.org/10.1016/bs.host.2020.12.002.

Szigeti, M., Ferenci, T., & Kovács, L. (2020). The use of block maxima method of extreme value statistics to characterise blood glucose curves. 2020 IEEE 15th International Conference of System of Systems Engineering (SoSE), 433–438. https://doi.org/10.1109/SoSE50414.2020.9130427.

Tian, A., Shu, X., Guo, J., Li, H., Ye, R., & Ren, P. (2023). Statistical modeling and dependence analysis for tide level via multivariate extreme value distribution method. Ocean Engineering, 286, https://doi.org/10.1016/j.oceaneng.2023.115616.

Towler, E., Llewellyn, D., Prein, A., & Gilleland, E. (2020). Extreme-value analysis for the characterization of extremes in water resources: A generalized workflow and case study on New Mexico monsoon precipitation. Weather and Climate Extremes, 29, https://doi.org/10.1016/j.wace.2020.100260.

Upadhyay, R. K. (2020). Markers for global climate change and its impact on social, biological and ecological systems: A review. American Journal of Climate Change, 9(03), 159. https://doi.org/10.4236/ajcc.2020.93012.

Zhang, Z., Huser, R., Opitz, T., & Wadsworth, J. (2022). Modeling spatial extremes using normal mean-variance mixtures. Extremes, 25(2), 175–197. https://doi.org/10.1007/s10687-021-00434-2.

Zhong, M., Zeng, T., Jiang, T., Wu, H., Chen, X., & Hong, Y. (2021). A copula-based multivariate probability analysis for flash flood risk under the compound effect of soil moisture and rainfall. Water Resources Management, 35, 83–98. https://doi.org/10.1007/s11269-020-02709-y.

Zscheischler, J., Martius, O., Westra, S., Bevacqua, E., Raymond, C., Horton, R. M., van den Hurk, B., AghaKouchak, A., Jézéquel, A., & Mahecha, M. D. (2020). A typology of compound weather and climate events. Nature Reviews Earth & Environment, 1(7), 333–347. https://doi.org/10.1038/s43017-020-0060-z.

DOI: https://doi.org/10.31764/jtam.v8i4.25436